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Journal Articles

1. Evolution  of multi-phase modes for nonlinear  dispersive waves, M.J. Ablowitz and D.J.  Benney,

Stud.  Appl.  Math.,  49 (1970) 225-238.

2.  Applications of slowly varying  nonlinear  dispersive  wave theories,  M.J.  Ablowitz,  Stud.  Appl.

Math.,  50 (1971) 329-344.

3.  Approximate methods  for obtaining  multi-phase modes in nonlinear  dispersive  wave problems, M.J.  Ablowitz,  Stud.  Appl.  Math., 51 (1972) 17-55.

4. Semi-resonant interactions and frequency  dividers,  M.J.  Ablowitz,  B.A. Funk  and A.C. Newell,

Stud.  Appl.  Math.,  52 (1973) 51-74.

5.  Decay of continuous  spectrum  for solutions  of Korteweg–deVries  equation,  M.J.  Ablowitz  and

A.C. Newell, J. Math.  Phys.,  14 (1973) 1277-1284.

 6. Method for solving Sine-Gordon equation,  M.J. Ablowitz, D.J. Kaup,  A.C. Newell and H. Segur,

Phys.  Rev.  Lett.,  30 (1973) 1262-1264

 7. Nonlinear-evolution equations  of physical  significance, M.J.  Ablowitz,  D.J.  Kaup,  A.C. Newell
      and H. Segur, Phys.  Rev.  Lett.,  31 (1973) 125-127.        

   8. Coherent pulse propagation, A dispersive,  irreversible  phenomenon,  M.J.  Ablowitz,  D.J.  Kaup, and A.C.  
Newell, J. Math.  Phys.,  11 (1974) 1852-1858.

   9. Inverse scattering transform - fourier analysis for nonlinear problems, M.J. Ablowitz, D.J. Kaup, A. C. Newell and H. Segur, Stud. Appl. Math., 53 (1974) 249-315. ∗This has been judged a citation classic by Current Contents (see Current Contents, June 7, 1982, Vol. 13, No. 23).

10.  Nonlinear  differential-difference  equations,  M.J.  Ablowitz  and J.F.  Ladik,  J. Math.  Phys.,  16

(1975) 598-603.

11.   Note  on resonance  and  nonlinear  dispersive  waves,  M.J.  Ablowitz,  Stud.   Appl.   Math.,  54

(1975) 61-70.

12.   Inverse  scattering transform - semi-infinite  interval,   M.J.  Ablowitz  and  H. Segur,  J. Math.

Phys., 16 (1975) 1054-1056.

13. Resonantly coupled nonlinear  evolution  equations,  M.J.  Ablowitz and R. Haberman, J. Math.

Phys.,  16 (1975) 2301-2305.

14.  Nonlinear  evolution  equations—2  and  3 dimensions,  M.J.  Ablowitz  and  R. Haberman, Phys.

Rev.  Lett.,  35 (1975) 1185-1188.

15. Asymptotic solutions and conservation  laws for the nonlinear  Schrodinger  equation  I,

H. Segur and M.J.  Ablowitz,  J. Math.  Phys.,  17 (1976) 710-713.

16. Nonlinear  differential–difference  equations  and fourier-analysis,  M.J.  Ablowitz and J.F.  Ladik,

J. Math.  Phys.,  17 (1976) 1011-1018.

17. Nonlinear  difference scheme and inverse scattering, M.J.  Ablowitz and J.F.  Ladik, Stud.  Appl.

Math.,  55 (1976) 213-229.

18.   Solution  of a class of nonlinear  partial difference equations,  M.J.  Ablowitz  and  J.F.  Ladik,

Stud.  Appl.  Math.,  57 (1977) 1-12.

19.   Nonlinear  evolution  equations,   continuous   and  discrete,  M.J.  Ablowitz,  SIAM  Review,  19

(1977) 663-684 (invited  article).

20. Asymptotic solutions  of Korteweg–deVries  equation,  M.J.  Ablowitz and H. Segur, Stud.  Appl.

Math.,  57 (1977) 13–44.

21. Exact  linearization of a Painlev´e transcendent, M.J.  Ablowitz and H. Segur, Phys.  Rev.  Lett.,

38 (1977) 1103-1106.

22. Solitons and rational solutions of non-linear evolution equations,  M.J. Ablowitz and J. Satsuma,

J. Math.  Phys.,  19 (1978) 2180-2186.

23. Lectures  on inverse scattering transform, M.J.  Ablowitz,  Stud.  Appl.  Math.,  58 (1978) 17–94.

24.    Non-linear  evolution  equations   and  ordinary   differential-equations  of Painlev´e  type,  M.J.

Ablowitz,  A. Ramani  and H. Segur, Lett.  al Nuovo Cimento,  23 (1978) 333–338.

25.  Note  on Miura  transformation, M.J.  Ablowitz,  M.D. Kruskal  and  H. Segur,  J. Math.   Phys.,

20 (1979) 999-1003.

26.  Evolution  of packets  of water-waves,  M.J.  Ablowitz  and  H. Segur, J. Fluid  Mech., 92  (1979)


27.  Explicit  solutions  of Fischer’s  equation  for a special wave speed,  M.J.  Ablowitz  and  A. Zep- petella,  Bulletin  of Math.  Bio., 41 (1979) 835-840.

28.  Transverse instability of one-dimensional  transparent optical  pulses in resonant  media,  M.J.

Ablowitz and Y. Kodama,  Phys.  Lett.  A, 70 (1979) 83-86.

29. 2-dimensional  lumps in nonlinear  dispersive systems,  J. Satsuma and M.J.  Ablowitz,  J. Math.

Phys.,  20 (1979) 1496-1503.

30.  Resonant  nonlinear  vibrations in continuous  systems.   I. Undamped  case, M.J.  Ablowitz,  A.

Askar, A.S. Cakmak  and H. Engin, Int.  J. Nonlin.  Mech., 14 (1979) 223-233.

31.  Resonant nonlinear  vibrations of continuous  systems.   II. Damped  and  transient-behavior,  H.

Engin, M.J. Ablowitz, A. Askar and A.S. Cakmak,  Int.  J. Nonlin.  Mech., 14 (1979) 235-246.

32. Solutions  of the Korteweg–deVries  equation,  M.J. Ablowitz and H. Cornille, Phys.  Lett.  A, 72

(1979) 277-280.

33. Internal wave-equation describing a stratified  fluid with finite depth,  J. Satsuma,

M.J. Ablowitz and Y. Kodama,  Phys.  Lett.  A, 73 (1979) 283-286.

34.  Solitary  wave collisions, M.J.  Ablowitz,  M.D. Kruskal  and  J.F.  Ladik,  SIAM J. Appl.  Math.,

36 (1979) 428-437.

35.   A connection  between  non-linear  evolution-equations and  ordinary  differential-equations  of

P-type. I., M.J.  Ablowitz,  A. Ramani  and H. Segur, J. Math.  Phys.,  21 (1980) 715-721.

36.   A connection  between  non-linear  evolution-equations and  ordinary  differential-equations  of

P-type. II., M.J.  Ablowitz,  A. Ramani  and H. Segur, J. Math.  Phys.,  21 (1980) 1006-1015.

37. Transverse instability of breathers in resonant media, Y. Kodama  and M.J. Ablowitz, J. Math.

Phys.,  21 (1980) 928-931.

38.  Comparison  between  finite-element  methods  and  spectral  methods  as applied  to bound-state problems,  M. Duff, H. Rabitz,  A.   Askar,  A. Cakmak  and  M.J.  Ablowitz,  J. Chem.  Phys., 72 (1980) 1543-1559.

39. Long internal  waves in fluids of great  depth,  M.J.  Ablowitz and H. Segur, Stud.  Appl.  Math.,

62 (1980) 249-262.

  40. Remarks on non-linear evolution-equations and ordinary  differential-equations of Painlev´e type, M.J.  Ablowitz,  Physica  D, 3 (1981) 129-141.
  41. Asymptotic solutions  of non-linear  evolution-equations and a Painlev´e transcendent, H. Segur and M.J.  Ablowitz,  Physica  D, 3 (1981) 165-184.

*42.  The  soliton:   A significant,  coherent  nonlinear  phenomena,  M.J.  Ablowitz  and  A.S. Fokas,

Clarkson  Innovations, 1 (1981) 2-3 (invited  article).

  43.  Finite  perturbations and some special solutions  of the Korteweg–deVries  equation,  H. Airault and M.J.  Ablowitz,  C.R.  Acad.  Sc.  Paris, 292  (1981) 279-281.

44. Non-linear intermediate long-wave equation  - Analysis and method  of solution,  Y. Kodama,  J.

Satsuma and M.J.  Ablowitz,  Phys.  Rev.  Lett.,  46 (1981) 687-690.

45. Linearization of the Korteweg–deVries and Painlev´e II equations,  A.S. Fokas and M.J. Ablowitz,

Phys.  Rev.  Lett.,  47 (1981) 1096-1100.

46.   Perturbations of solitons  and  solitary  waves,  Y. Kodama  and  M.J.  Ablowitz,  Stud.   Appl.

Math.,  64 (1981) 225-245.

47. The periodic cubic Schr¨odinger-equation, Y.C. Ma and M.J.  Ablowitz,  Stud.  Appl.  Math.,  65

(1981) 113-158.

48.  Note on asymptotic solutions  of the  Korteweg–deVries  equation  with  solitons,  M.J.  Ablowitz and Y. Kodama,  Stud.  Appl.  Math.,  66 (1982) 159-170.

49.  Direct and  inverse scattering problems  of the  non-linear  intermediate long-wave equation,  Y.

Kodama,  M.J.  Ablowitz and J. Satsuma, J. Math.  Phys.,  23 (1982) 564-576.

50.  On the  periodic intermediate long-wave equation,  M.J.  Ablowitz,  A.S. Fokas,  J. Satsuma and

H. Segur, J. Phys.  A - Math.  and Gen.,  15 (1982) 781-786.

51.  Direct  linearizations of the  Korteweg-deVries  equations,  A.S. Fokas  and  M.J.  Ablowitz,  AIP Conference  Proceedings,  88 (1982) 237-241.

52.  A direct  linearization associated  with  the  Benjamin-Ono-Equation, M.J.  Ablowitz  and  A.S.

Fokas,  AIP  Conference  Proceedings,  88 (1982) 229-236.

53. On a unified approach to transformations and elementary solutions of Painlev´e equations,  A.S.

Fokas and M.J.  Ablowitz,  J. Math.  Phys.,  23 (1982) 2033-2042.

  54. The inverse scattering transform for the Benjamin-Ono-Equation - A pivot to multidimensional problems,  A.S.        Fokas and M.J.  Ablowitz,  Stud.  Appl.  Math.,  68 (1983) 1-10.
 55.    On  the  inverse  scattering of the  time-dependent  Schrodinger  equation  and  the  associated Kadomsev-Petviashvili  equation,   A.S.  Fokas  and  M.J.  Ablowitz,  Stud.   Appl.   Math.,  69 (1983) 211-228.

 56.  On the  inverse scattering transform for the  Kadomtsev-Petviashvili equation,  M.J.  Ablowitz, D. Bar Yaacov and A.S. Fokas,  Stud.  Appl.  Math.,  69 (1983) 135-143.

 57.  Method  of solution  for a class of multidimensional non-linear  evolution-equations, A.S. Fokas and M.J.  Ablowitz,  Phys.  Rev.  Lett.,  51 (1983) 7-10.

58. On the initial-value problem  of the 2nd Painlev´e transcendent, A.S. Fokas and M.J.  Ablowitz,

Commun.  Math.  Phys.,  91 (1983) 381-403.

  59.  The  direct  linearizing  transform and  the  Benjamin-Ono  equation,  M.J.  Ablowitz,  A.S. Fokas and R.L. Anderson,  Phys.  Lett.  A, 93 (1983) 375-378.
  60.   On  the  inverse  scattering and  direct  linearizing  transforms   for the  Kadomtsev-Petviashvili equation,  A.S. Fokas and M.J.  Ablowitz,  Phys.  Lett.  A, 94 (1983) 67-70.

61.  The  inverse  scattering transform for multidimensional (2+1)  problems,  A.S. Fokas  and  M.J.

Ablowitz,  Lect.  Notes Phys.,  189  (1983) 137-183.

62. Comments  on the inverse scattering transform and related non-linear,  evolution-equations, M.J.

Ablowitz and A.S. Fokas,  Lect.  Notes Phys.,  189  (1983) 3-24.

63. On a Backlund  transformation and scattering problem for the modified intermediate long-wave equation,  J. Satsuma, T.R.  Taha  and M.J.  Ablowitz,  J. Math.  Phys.,  25 (1984) 900-904.

64. Analytical  and numerical  aspects  of certain  nonlinear  evolution-equations.  I. Analytical, T.R.

Taha  and M.J.  Ablowitz,  J. Comp.  Phys.,  55 (1984) 192-202.

  65.   Analytical   and  numerical  aspects  of certain  nonlinear  evolution-equations.   II.  Numerical, nonlinear  Schr¨odinger-Equation, T.R.  Taha  and M.J.  Ablowitz,  J. Comp.  Phys.,  55 (1984)


  66.   Analytical   and  numerical  aspects  of certain  nonlinear  evolution-equations.   III.  Numerical, Korteweg–deVries  equation,  T.R.  Taha  and M.J.  Ablowitz,  J. Comp.  Phys.,  55 (1984) 231-253.
 67. On the inverse scattering transform of multidimensional nonlinear equations  related to 1
st -order systems in the plane,  A.S. Fokas and M.J.  Ablowitz,  J. Math.  Phys.,  25 (1984) 2494-2505.

68.   On  the  limit  from  the  intermediate long-wave  equation  to  the  Benjamin-Ono   equation,   P.

Santini,  M.J.  Ablowitz and A.S. Fokas,  J. Math.  Phys.,  25 (1984) 892-899.

  69. The direct linearization of a class of nonlinear evolution-equations, P.M. Santini,  M.J. Ablowitz, and A.S. Fokas,  J. Math Phys.,  25 (1984) 2614-2619.

70.  A multidimensional inverse-scattering method,  A. Nachman  and  M.J.  Ablowitz,  Stud.  Appl.

Math.,  71 (1984) 243-250.

71.   Multidimensional inverse  scattering for 1st -order  systems,  A. Nachman  and  M.J.  Ablowitz,

Stud.  Appl.  Math.,  71 (1984) 251-262.

  72.  Nonlinear  evolution-equations associated  with  a Riemann-Hilbert scattering problem,  A. De- gasperis, P.M.  Santini  and M.J.  Ablowitz,  J. Math.  Phys.,  26 (1985) 2469-2472.

73. Multidimensional nonlinear  evolution-equations and inverse scattering, M.J. Ablowitz and A.I.

Nachman,  Physica  D, 18 (1986) 223-241.

  74. On the solution of the generalized wave and generalized Sine-Gordon equations,  M.J. Ablowitz, R. Beals and K. Tenenblat, Stud.  Appl.  Math.,  74 (1986) 177-203.
 75. Note on solutions  to a class of nonlinear  singular  integrodifferential equations,  M.J.  Ablowitz, A.S. Fokas and M.D. Kruskal,  Phys.  Lett A, 120  (1987) 215-218.

 76.  An example  of a ¯ problem  arising  in a finite difference context:   Direct and  inverse problem for the  discrete  analogue  of the  equation  ψxx + U ψ = σψy , O. Ragnisco,  P.M.  Santini,  S. Chitlaru–Briggs and M.J.  Ablowitz,  J. Math.  Phys.,  28 (1987) 777-780.

77.    Solutions  of multidimensional extensions  of the  anti-self-dual   Yang-Mills  equation,     M.J.

Ablowitz,  D.G. Costa  and K. Tenenblat, Stud.  Appl.  Math.,  77 (1987) 37-46.

  78.   On  the  initial-value problem  for a  class of nonlinear  integral  evolution-equations including the Sine-Hilbert  equation,  P.M.  Santini,  M.J.  Ablowitz and A.S. Fokas,  J. Math.  Phys.,  28 (1987) 2310-2316.
 79.  Davey-Stewartson-I system  - A quantum (2+1)  dimensional  integrable  system,  C.L. Schultz, M.J.  Ablowitz and D. Bar Yaacov, Phys.  Rev.  Lett.,  59 (1987) 2825-2828.

80.   A method  of linearization for Painlev´e  equations  - Painlev´e-IV,  Painlev´e-V,  A.S. Fokas,  U.

Mugan and M.J.  Ablowitz,  Physica  D, 30 (1988) 247-283.

81.   A  rule  for  fast  computation and  analysis  of soliton  automata, T.S.  Papatheodorou,  M.J.

Ablowitz and Y.G. Saridakis,  Stud.  Appl.  Math.,  79 (1988) 173-184.

82.   Analytical   and  numerical  aspects  of certain  nonlinear  evolution-equations.   IV.  Numerical, modified  Korteweg–deVries  equation,   T.  Taha  and  M.J.  Ablowitz,  J. Comp.    Phys.,  77 (1988) 540-548.

83.  Hodograph  transformations of linearizable  partial-differential equations,  P.A.  Clarkson,  A.S.

Fokas and M.J.  Ablowitz,  SIAM J. Appl.  Math.,  49 (1989) 1188-1209.

84. Forced nonlinear  evolution-equations and the inverse scattering transform, A.S. Fokas and M.J.

Ablowitz,  Stud.  Appl.  Math.,  80 (1989) 253-272.

85.  Interaction of simple particles  in soliton  cellular  automata, A.S. Fokas,  E.P.  Papadopoulou, Y.G. Saridakis  and M.J.  Ablowitz,  Stud.  Appl.  Math.,  81 (1989) 153-180.

86. Strong coupling limit of certain  multidimensional nonlinear-wave  equations,  M.J. Ablowitz and

C.L. Schultz,  Stud.  Appl.  Math.,  80 (1989) 229-238.

87. Numerically induced chaos in the nonlinear Schrodinger-Equation, B. Herbst and M.J. Ablowitz,

Phys.  Rev.  Lett.,  62 (1989) 2065-2068.

88.   Action  angle  variables  and  trace  formula  for D-bar  limit  case of Davey-Stewartson I, C.L.

Schultz  and M.J.  Ablowitz,  Phys.  Lett.  A., 135  (1989) 433-437.

89.  Solitons,  inverse  problems  and  nonlinear  equations,  M.J.  Ablowitz,  Math.   Applic.  Comp.,  8

(1989) 127-152 (invited  article).

90. On homoclinic structure and numerically  induced chaos for the nonlinear Schrodinger-Equation, M.J.  Ablowitz and B.M. Herbst,  SIAM J. Appl.  Math.,  50 (1990) 339-351.

91. Reductions  of self-dual Yang-Mills fields and classical-systems,  S. Chakravarty, M.J.  Ablowitz and P.A.  Clarkson,  Phys.  Rev.  Lett.,  65 (1990) 1085-1087.

92. On the boundary-conditions of the Davey-Stewartson equation,  M.J.  Ablowitz,  S.V. Manakov and  C.L.  Schultz,  Phys.   Lett.   A, 148  (1990) 50-52; condensed  version  published  in Non- linear  Evolution  Equations  and Dynamical  Systems pp 29-32, Research  Reports  in Physics, Springer-Verlag,  Berlin (1990).

93.   On  the  Kadomtsev-Petviashvili  equation  and  associated  constraints, M.J.  Ablowitz  and  J.

Villarroel,  Stud.  Appl.  Math.,  85 (1991) 195-213.

94.    On  the  hamiltonian-formalism for  the  Davey-Stewartson system,  J.  Villarroel  and    M.J.

Ablowitz,  Inverse  Problems,  7 (1991) 451-460.

95. Numerical homoclinic instabilities and the complex modified Korteweg-de Vries equation,  B.M.

Herbst,  M.J.  Ablowitz and E. Ryan,  Computer  Phys.  Commun.,  65 (1991) 137-142.

96.  Forced  and semiline solutions  of the  Burger’s-Equation, M.J.  Ablowitz  and S. De Lillo, Phys.

Lett.  A, 156  (1991) 483-487.

97.  Class  of stable  multistate time-reversible  cellular  automata with  rich  particle  content, M.J.

Ablowitz,  J.M.  Keiser and L.A. Takhtajan, Phys.  Rev.  A, 44 (1991) 6909-6912.

98.   Dynamics  of semi-discretizations of the  defocusing  nonlinear  Schrodinger  equation,     M.J.

Ablowitz,  B.M. Herbst  and J.A.  Weidman,  IMA J. Num.  Anal.  II, (1991) 539-552.

99. On the method  of solution  to the 2 + 1 Toda  equation,  J. Villarroel and M.J.  Ablowitz,  Phys.

Lett.  A, 163  (1992) 293-298.

100.  A new Hamiltonian amplitude equation  governing  modulated wave instabilities, M. Wadati, H. Segur and M.J.  Ablowitz,  J. Phys.  Soc.  of Japan, 61 (1992) 1187-1193.

*101.   Numerical  homoclinic  instabilities in  the  Sine-Gordon  equation,   B.M.  Herbst  and  M.J.

Ablowitz,  Quaestiones  Math.,  15 (1992) 345-363.

*102.    Stable,   multi-state,  time-reversible   cellular  automata with  rich  particle   content,    M.J.

Ablowitz,  J.M.  Keiser and L.A. Takhtajan, Quaestiones  Math.,  15 (1992) 325-343.

103.  Interaction effects on wavelength  multiplexed  soliton  data  packets,  A.F.  Benner,  J.R.  Sauer and M.J.  Ablowitz,  J. Opt.  Soc.  Amer.  B - Opt.  Phys.,  10, (1993) 2331-2340.

104.  A self-dual Yang-Mills hierarchy  and  its reductions  to integrable  systems  in 1 + 1 and  2 + 1 dimensions,  M.J.  Ablowitz,  S. Chakravarty and  L.A. Takhtajan, Commun.   Math.   Phys.,

158  (1993) 289-314.

105.   Numerical  chaos,  symplectic  integrators and  exponentially   small  splitting  distances,   B.M.

Herbst  and M.J.  Ablowitz,  J. Comp.  Phys.,  105  (1993) 122-132.

106. On the inverse scattering transform of the 2+1 Toda equation,  J. Villarroel and M.J. Ablowitz,

Physica  D, 65 (1993) 48-70.

107.  Numerical  chaos, roundoff errors,  and  homoclinic manifolds,  M.J.  Ablowitz,  C. Schober and

B.M. Herbst,  Phys.  Rev.  Lett.,  71 (1993) 2683-2686.

108.   On  the  method  of solution  of the  differential-delay  Toda  equation,   J.  Villarroel  and  M.J.

Ablowitz,  Phys.  Lett.  A, 180  (1993) 413-418.

109. Solutions to the 2+1 Toda equation,  J. Villarroel and M.J. Ablowitz, J. Phys.  A - Math.  and

Gen.,  27 (1994) 931-941.

110. Parametric forcing, bound-states and solutions of a nonlinear  Schrodinger  type equation,  M.J.

Ablowitz and S. De Lillo, Nonlinearity, 7 (1994) 1143-1153.

111. Wave collapse and instability of solitary  waves of a generalized  Kadomtsev-Petviashvili equa- tion, X.P.  Wang,  M.J.  Ablowitz and H. Segur, Physica  D, 78 (1994) 241-265.

112.    Homoclinic  manifolds  and  numerical  chaos  in  the  nonlinear   Schrodinger-Equation, M.J.

Ablowitz and C. Schober, Math.  and Comp.  Sim., 37 (1994) 249-264.

113. Symplectic methods  for the nonlinear  Schrodinger-Equation, B.M Herbst,  F. Varadi  and M.J.

Ablowitz,  Math.  and Comp.  Sim., 37 (1994) 353-369.

*114. Effective chaos in the nonlinear  Schrodinger  equation,  M.J.  Ablowitz and C. Schober,  Con- temp.  Math.,  172  (1994) 253-268.

115.   Hamiltonian integrators for the  nonlinear  Schrodinger  equation,   M.J.  Ablowitz  and  C.M.

Schober, Intern. J. Mod.  Phys.  C - Phys.  and Comp., 5 (1994) 397-401.

116. Multisoliton  interactions and wavelength-division multiplexing, S. Chakravarty, M.J. Ablowitz, J.R.  Sauer and R.B. Jenkins,  Opt.  Lett.,  20 (1995) 136-138.

117. Integrability, computation and applications, M.J. Ablowitz, S. Chakravarty and B.M. Herbst,

Acta Applicande  Mathematicae, 39 (1995) 5-37.

118.   Data-dependent  timing  jitter   in  wavelength-dependent-multiplexing soliton  systems,  R.B.

Jenkins,  J.R.  Sauer, S. Chakravarty and M.J.  Ablowitz,  Opt.  Lett.,  20 (1995) 1964-1966.

119. Numerical-simulation of quasi-periodic  solutions of the Sine-Gordon  equation,  M.J. Ablowitz, B.M. Herbst  and C.M. Schober, Physica  D, 87 (1995) 37-47.

120.   Numerical  stochasticity, hamiltonian integrators, and  the  nonlinear  Schrodinger-Equation, M.J.  Ablowitz  and  C. Schober,  Three-Dim.  Sys.–Annals  NY Acad.   Sci.,  751  (1995) 162-


121.   Integrability,  monodrom evolving  deformations,  and  self-dual  Bianchi  IX  systems,      S.

Chakravarty and M.J.  Ablowitz,  Phys.  Rev.  Lett.,  76 (1996) 857-860.

122.   Computational chaos  in the  nonlinear  Schrodinger  equation  without  homoclinic  crossings, M.J.  Ablowitz,  B.M. Herbst  and C.M. Schober, Physica  A, 228  (1996) 212-235.

123.   On  the  numerical  solution  of the  Sine-Gordon  equation.    I. Integrable   discretizations and homoclinic manifolds, M.J.  Ablowitz, B.M. Herbst and C.M. Schober, J. Comp.  Phys., 126 (1996) 299-314.

124.  The  Burgers  equation  under  deterministic and  stochastic  forcing, M.J.  Ablowitz  and  S. De

Lillo, Physica  D, 92 (1996) 245-259.

125.  On a 2+1  Volterra  system,  J. Villarroel,  S. Chakravarty and  M.J.  Ablowitz,  Nonlinearity, 9

(1996) 1113-1128.

126.  Four-wave  mixing in wavelength-division-multiplexed soliton  systems:  damping  and  amplifi- cation,  M.J. Ablowitz, G. Biondini, S. Chakravarty, R.B. Jenkins  and J.R. Sauer, Opt.  Lett.,

21 (1996) 1646-1648.

127. Solutions to the time dependent Schrodinger  and the Kadomtsev-Petviashvili equations,  M.J.

Ablowitz and J. Villarroel,  Phys.  Rev.  Lett.,  78 (1997) 570-573.

128.  The nonlinear  Schr¨odinger equation:   asymmetric perturbations,  traveling  waves and  chaotic structures, M.J.  Ablowitz,  B.M.  Herbst  and  C.M.  Schober,  Math.   and  Comp.   Sim.,  43 (1997) 3-12.

129. Initial time layers and Kadomtsev-Petviashvili-Type equations,  M.J. Ablowitz and X-P. Wang,

Stud.  Appl.  Math.,  98 (1997) 121-137.

130.  On the well-posedness of the Eckhaus  equation,  M.J.  Ablowitz,  G. Biondini  and S. De Lillo,

Phys.  Lett.  A, 230  (1997) 319-323.

131. On the numerical solution of the Sine-Gordon equation.  II. Performance  of numerical schemes, M.J.  Ablowitz,  B.M. Herbst  and C.M. Schober, J. of Comp.  Phys.,  131  (1997) 354-367.

132.    Four-wave   mixing  in  wavelength-division-multiplexed  soliton  systems:    ideal  fibers,  M.J.

Ablowitz,  G.  Biondini,  S. Chakravarty, R.B.  Jenkins  and  J.R.  Sauer,  J. Opt.   Soc.   Am. B., 14 (1997) 1788-1794.

133. Multi-dimensional pulse propagation in non-resonant χ(2) materials, M.J. Ablowitz, G. Bion- dini and S. Blair, Phys.  Lett.  A, 236  (1997) 520-524.

134. On timing  jitter  in wavelength-division multiplexed  soliton systems,  M.J.  Ablowitz,  G. Bion- dini, S. Chakravarty and R.L. Horne, Opt.  Comm.,  150  (1998) 305-318.

135.  Multiscale  pulse  dynamics  in communication systems  with  strong  dispersion  management, M.J.  Ablowitz and G. Biondini,  Opt.  Lett.,  23 (1998) 1668-1670.

*136.    The  generalized  Chazy  equation   and  Schwarzian   triangle   functions,   M.J.  Ablowitz,   S.

Chakravarty and R. Halburd,  Asian  J. Math.,  2 (1998) 619-624.

137. On discretizations of the vector nonlinear  Schrodinger  equation,  M.J.  Ablowitz,  Y. Ohta  and

A.D. Trubatch, Phys.  Lett.  A, 253  (1999) 287-304.

138. The generalized Chazy equation from the self-duality equations,  M.J. Ablowitz, S. Chakravarty and R. Halburd,  Stud.  Appl.  Math.,  103  (1999) 75-88.

139.  On the  discrete  spectrum  of the  nonstationary Schrodinger  equation  and multipole  lumps  of the  Kadomtsev-Petviashvili I equation,  J.  Villarroel  and  M.J.  Ablowitz,  Commun.   Math. Phys.,  207  (1999) 1-42.

140. A comparison between lumped and distributed filter models in wavelength-division multiplexed soliton  systems,  M.J.  Ablowitz,  G. Biondini,  S. Chakravarty and  R. Horne,  Opt.   Comm.,

172  (1999) 211-227.

141.  Solitons and  symmetries,  M.J.  Ablowitz  and  P.A.  Clarkson,  J. Eng.  Math.,  Special Edition, M.J.  Ablowitz and P.A.  Clarkson,  editors,  36 (1999) 1-9.

142.  Modulated periodic Stokes waves in deep water,  M.J.  Ablowitz,  J. Hammack,  D. Henderson and C.M. Schober, Phys.  Rev.  Lett.,  84 (2000) 887-890.

143. On integrability and chaos in discrete  systems,  M.J.  Ablowitz,  Y. Ohta,  and A.D. Trubatch,

Chaos,  Solitons and Fractals, 11 (2000) 159-169.

144.  A novel class of solutions  of the  non-stationary Schrodinger  and the  Kadomtsev-Petviashvili

I equations,  M.J. Ablowitz, S. Chakravarty, A.D. Trubatch and J. Villarroel, Phys.  Lett.  A,

267  (2000) 132-146.

145. On a Burgers-Stefan problem, M.J. Ablowitz and S. De Lillo, Nonlinearity, 13 (2000) 471-478.

146. On the extension  of the Painlev´e property to difference equations,  M.J. Ablowitz, R. Halburd and B. Herbst,  Nonlinearity, 13 (2000) 889-905.

147. Optical  solitons:  perpsectives  and applications, M.J. Ablowitz, G. Biondini and L. Ostrovsky,

Chaos, 10 (2000) 471-474.

148.  Solutions  of a Burgers-Stefan problem,  M.J.  Ablowitz  and  S. De Lillo, Phys.  Lett.  A., 271

(2000) 273-276.

149.   Resonant  nonlinear  intrachannel interactions in  strongly  dispersion-managed transmission systems,  M.J.  Ablowitz and T. Hirooka, Opt.  Lett.,  25 (2000) 1750-1752.

150.   Quasi-linear   optical  pulses  in  strongly  dispersion-managed transmission  systems,    M.  J.

Ablowitz,  T. Hirooka and G. Biondini,  Opt.  Lett.,  26 (2001) 459-461.

151.  Long-time  dynamics  of the  modulational instability of deep water  waves, M.J.  Ablowitz,  J.

Hammack,  D.  Henderson  and  C.M.  Schober,  Physica  D - Nonlin.   Phenom., 152  (2001)


152. Nonlinear Schr¨odinger equations  with mean terms in nonresonant multidimensional quadratic materials, M.J. Ablowitz, G. Biondini and S. Blair, Phys.  Rev.  E, 63 (2001) 046605-605-620.

153.  Incomplete  collisions of wavelength-division  multiplexed  dispersion-managed solitons,  M.J.

Ablowitz, G. Biondini and E.S. Olson J. Opt.  Soc.  Am.  B - Opt.  Phys., 18 (2001) 577-583.

154. Nonlinear  feedback shift registers  via nonlinear  evolution,  M.J.  Ablowitz,  Stud.  Appl.  Math.,

107  (2001) 127-136.

155.  Nonlinear  effects in quasi-linear  dipersion-managed pulse  transmission, M.J.  Ablowitz  and

T.Hirooka,  IEEE  Phot.  Tech.  Lett.,  13 (2001) 1082-1084.

156.  Intrachannel pulse interactions in dispersion-managed transmission systems:  timing  shifts  , M.J.  Ablowitz and T.Hirooka,  Opt.  Lett.,  26 (2001) 1846-1848.

157.  Discrete  diffraction  managed  spatial  solitons,  M.J.  Ablowitz  and  Z. Musslimani,  Phys.  Rev.

Lett.,  87 (2001) 254102-1-4.

158.  Discretizations, integrable  systems  and  computation, M.J.  Ablowitz,  B.M. Herbst  and  C.M.

Schober, J. Phys.  A - Math.  and Gen.,  34 (2001) 10671-10693.

159. Localized multi-dimensional optical pulses in non-resonant quadratic materials, M.J. Ablowitz, G. Biondini  and S. Blair, Math.  and Comp.  Sim., 56 (2001) 511-519.

160.   Methods  for discrete  solitons  in  nonlinear  lattices,   M.J.  Ablowitz,  Z. Musslimani  and  G.

Biondini,  Phys.  Rev.  E, 65 (2002) 026602-1-4.

161. Intrachannel pulse interactions in dispersion-managed transmission systems:  energy transfer, M.J.  Ablowitz and T. Hirooka, Opt.  Lett.,  27 (2002) 203-205.

162.   Managing  nonlinearity  in  strongly  dispersion-managed  optical  pulse  transmission,   M.J.

Ablowitz and T.Hirooka,  J. Opt.  Soc.  Amer.  B - Opt.  Phys.,  19 (2002) 425-439.

163.   Collision-induced  timing  shifts  in  dispersion-managed soliton  systems,  M.J.  Ablowitz,  A.

Biswas,  A. Docherty,  T.Hirooka,   G.  Biondini  and  S. Chakravarty, Opt.   Lett.,  27  (2002)


164.  Suppression  of intrachannel dispersion-managed pulse interactions by distributed  amplifica- tion, T.Hirooka  and M.J.  Ablowitz,  IEEE  Phot.  Tech.  Lett.,  14 (2002) 316-318.

165.  Analysis  of timing  and  amplitude jitter  due to intrachannel dispersion-managed pulse inter- actions,  T.Hirooka  and M.J.  Ablowitz,  IEEE  Phot.  Tech.  Lett.,  14 (2002) 633-635.

166. Discrete  vector  spatial  solitons in a nonlinear  waveguide array,  M.J.  Ablowitz and Z. Mussli- mani, Phys.  Rev.  E, 65 (2002) 056618-1-13.

167.  Resonant  intrachannel pulse interactions in dispersion-managed transmission systems,  M.J.

Ablowitz and T.Hirooka,  IEEE  Journal on Selected Topics in Quantum  Electronics, 8(2002)


168. Higher order asymptotic analysis  of dispersion-managed transmission systems:  solutions  and their  characteristics, M.J.  Ablowitz,  T.Hirooka  and  T.  Inoue,  J. Opt.  Soc.  Am.  B - Opt. Phys.,  19 (2002) 2876-2885.

169. The Cauchy  problem  for the Kadomtsev-Petviashili II equation  with nondecaying  data  along a line, J. Villarroel and M.J.  Ablowitz,  Stud.  Appl.  Math.,  109  (2002) 151-162.

170.  Dark  and  gray strong  dispersion-managed solitons,  M.J.  Ablowitz  and  Z. Musslimani,  Phys.

Rev.  E, 67 (2003) 025601-1-4.

171. Four-wave  mixing in dispersion-managed return-to-zero systems,  M.J.  Ablowitz,  G. Biondini, S. Chakravarty and R.L. Horne, J. Opt.  Soc.  Am.  B - Opt.  Phys.,  20 (2003) 831-845.

172. On a two-phase free boundary problem,  M.J.  Ablowitz and S. De Lillo, J. of Phys.  A: Math. and Gen.,  36 (2003) 4307-4319.

173.  Incomplete  collisions in strongly  dispersion-managed return-to-zero communication systems, M.J.  Ablowitz,  A. Docherty  and T. Hirooka, Opt.  Lett.,  28 (2003) 1191-1193.

174.  Discrete  spatial  solitons  in a diffraction-managed nonlinear  waveguide  array:   a unified  ap- proach,  M.J.  Ablowitz  and  Z.  Musslimani,  Physica  D  -  Nonlin.    Phenom., 184,   (2003)


175.  On the  discrete  spectrum  of systems  in the  plane  and  the  Davey-Stewartson II equation,  J.

Villarroel and M.J.  Ablowitz,  SIAM J. Math.  Anal.,  34 (2003) 1253-1278.

176.  Integrable  systems  and  reductions  of the  self-dual  Yang-Mills  equations,  M.J.  Ablowitz,  S.

Chakravarty and R.G. Halburd,  J. Math.  Phys.,  44 (2003) 3147-3173.

177. Dispersion  management for randomly  varying  optical  fibers, M.J.  Ablowitz and J.T.  Moeser,

Opt.  Lett.,  29 (2004) 821-823.

178. Carrier-envelope phase slip of ultrashort dispersion- managed  solitons, M.J. Ablowitz, B. Ilan and S. Cundiff, Opt.  Lett.,  29 (2004) 1808-1810.

179.  On the  initial  value problem  for the  KPII  equation  with  data  that does not  decay along a line, J. Villarroel and M.J. Ablowitz, Nonlinearity, 17 (2004) 1843-1866. * in journal  article, Ablowitz was incorrectly  spelled as “Abowitz”

180.  Reduction  of collision-induced  timing  shifts in dispersion-managed quasi-linear  systems  with periodic  group-delay  dispersion  compensation, M.J.  Ablowitz,  C. Ahrens,  G.  Biondini,  S. Chakravarty and A. Docherty,  Opt.  Lett.,  29 (2004) 2354-2356.

181. Soliton interactions in the vector NLS equation,  M. J. Ablowitz, B. Prinari and A.D. Trubatch,

Inverse  Prob.,  20 (2004) 1217-1237.

182.   Integrable   nonlinear  Schr¨odinger  systems  and  their  soliton  dynamics,  M.J.  Ablowitz,  B.

Prinari and A.D.Trubatch, Dynam.  Part. Diff. Eq., 1 (2004) 239-299.

183.   Solvability  of the  direct  and  inverse  problems  for the  nonlinear  Schrodinger  equation,   J.

Villarroel,  M.J.  Ablowitz and B. Prinari, Acta Applic.  Math.,  87 (2005) 245-280.

184. Dynamics  of nonlinear  and dispersion  managed  solitons,  Q. Quraishi,  S. Cundiff, B. Ilan and

M.J.  Ablowitz,  Phys.  Rev.  Lett.,  94 (2005) 243904.

185. Spectral  renormalization method  for computing  self-localized solutions  to nonlinear  systems, M.J.  Ablowitz and Z. Musslimani,  Opt.  Lett.,  30 (2005) 2140-2142.

186. On a ”quasi” integrable  discrete Eckhaus equation,  M.J. Ablowitz, C.D. Ahrens and S. DeLillo,

J. of Nonlin.  Math.  Phys.,  12 (2005) 1-12.

187.  Wave dynamics  in optically  modulated waveguide arrays,  M.J.  Ablowitz,  K. Julien,  Z. Mus- slimani and M. Weinstein,  Phys.  Rev.  E, 71 (2005) 055602.

188.   Periodic-group-delay  dispersion  compensation  reduces  collision-induced  timing  shifts    in dispersion-managed  quasilinear   systems,   M.J.  Ablowitz,   C.  Ahrens,   G.  Biondini,         S. Chakravarty and A. Docherty,  Theor.  and Math.  Phys.,  144  (2005) 881-887.

189. Calculation, characterization, and application of the time shift function in wavelength-division- multiplexed  return-to-zero systems,  O.V.  Sinkin,  V.S. Gregorian,  J.  Zweck, C.R.  Menyuk, A. Docherty  and M.J Ablowitz,  Opt.  Lett.,  30 (2005) 2056-2058.

190. Wave collapse in a class of nonlocal nonlinear Schrodinger equations,  M.J. Ablowitz, I. Bakirtas and B. Ilan, Physica  D - Nonlin.  Phenom., 207  (2005) 230-253.

191.   Asymptotic  analysis  of collision-induced  timing  shifts  in  return-to-zero quasi-linear   sys- tems  with  pre-dispersion  and  post-dispersion compensation, C.D.  Ahrens,  M.J.  Ablowitz, A. Docherty,  O.V. Sinkin, V. Gregorian  and C.R. Menyuk, Opt.  Lett.,  31 (2006) 5-7.

192. Theory of magnetodynamics induced by spin torque in perpendicularly magnetized  thin films, M.A.  Hoefer,  M.J.  Ablowitz,  B. Ilan,  M.R.  Pufall,  and  T.J.  Silva,  Phys.   Rev.   Lett.,  95 (2005) 267206.

193.    Discrete  vector  solitons:   Composite  solitons,  YangBaxter  maps  and  computation, M.J.

Ablowitz,  B. Prinari and A.D. Trubatch, Stud.  Appl.  Math.,  116  (2006) 97-133.

194. Inverse scattering transform for the vector nonlinear  Schrodinger  equation  with nonvanishing boundary conditions,  B. Prinari, M.J. Ablowitz and G. Biondini,  J. Math.  Phys., 47 (2006)


195.   Noise-induced  linewidth  in frequency  combs,  M.J.  Ablowitz,  B.  Ilan  and  S. Cundiff,  Opt.

Lett.,  31 (2006) 1875-1877.

196. On a new non-local formulation of water waves, M.J. Ablowitz, A.S. Fokas and Z. Musslimani,

J. of Fluid Mech., 562  (2006) 313-343.

197.  Solitons  in two-dimensional lattices  possessing defects,  dislocations,  and  quasicrystal struc- tures,  M. J.  Ablowitz,  B. Ilan,  E.  Schonbrun, and  R.  Piestun, Phys.   Rev.   E,  74  (2006) 035601.

198.  Dispersive  and  classical shock waves in Bose-Einstein  condensates  and  gas dynamics,  M.A.

Hoefer, M.J.  Ablowitz,  I. Coddington, E.A.  Cornell,  P.  Engels and  V. Schweikhard,  Phys. Rev.  A., 74 (2006) 023623.

199. Integrable  systems and modular  forms of level 2, M.J. Ablowitz, S. Chakravarty and H. Hahn,

J. of Phys.  A - Math.  and Gen.,  39 (2006) 15341-15353.

200. Two-dimensional solitons in irregular  lattice  systems,  M. J. Ablowitz,  B. Ilan, E. Schonbrun, and R. Piestun, Theor.  Math.  Phys.,  151  (2007) 723-734.

201.  Inverse  scattering transform for the  integrable  discrete  nonlinear  Schrodinger  equation  with nonvanishing  boundary conditions,  M.J. Ablowitz, G. Biondini and B. Prinari, Inverse Prob.,23 (2007) 1711-1758.

202. Interactions of dispersive  shock waves, M.A. Hoefer and M.J.  Ablowitz,  Physica  D - Nonlin.

Phenom., 236  (2007) 44-64.

203.  On a class of nonlocal nonlinear  Schrodinger  equations  and  wave collapse, M.J.  Ablowitz,  I.

Birkitas  and B. Ilan, Eur.  Phys.  J.-  Spec.  Top.,  147  (2007) 343-362.

204. Piston  dispersive shock wave problem,  M.A. Hoefer, M.J. Ablowitz and P. Engels, Phys.  Rev.

Lett.,  100,  (2008) 084504.

205.  Solitons in dispersion-managed mode-locked lasers, M.J.  Ablowitz,  T.P.  Horikis and B. Ilan,

Phys.  Rev.  A, 77 (2008) 033814.

206.  Pulse  dynamics  and  solitons  in mode-locked  lasers,  M.J.  Ablowitz  and  T.P.  Horikis,  Phys.

Rev.  A, 78 (2008) 011802.

207.   Spectral  formulation of the  two  fluid  Euler  equations   with  a  free surface  and  long  wave reductions, M.J.  Ablowitz and T. S. Haut,  Analysis and Applications,  6 (2008) 323-348.

208.   Damping  of periodic  waves  in  physically  significant  wave  systems,  M.J.  Ablowitz,    S.A.

Ablowitz and N. Antar,  Stud.  Appl.  Math.  121  (2008) 313-335.

209. Solitons in optics and water waves, M.J. Ablowitz, Mathematics Today,  (April, 2008), 198-200.

210. Asymptotic Analysis of Pulse Dynamics in Mode-locked Lasers, Mark J. Ablowitz, Theodoros

P. Horikis, Sean D. Nixon and Yi Zhu, Stud.  Appl.  Math.  122  (2009) 411-425.

211.  Conical  Diffraction  in Honeycomb  lattices,  Mark  J.  Ablowitz,  Sean D. Nixon and  Yi Zhu,

Physical  Review A, 79 (2009) 053830

212. Soliton Generation and Multiple Phases in Dispersive Shock and Rarefaction Wave Interaction, M. J. Ablowitz,  D.E. Baldwin,  and M. A. Hoefer, Physical  Review E, 80 (2009) 016603

213. Solitons and spectral  renormalization methods  in nonlinear  optics,  M. J. Ablowitz and T. P.

Horikis, Eur.  Phys.  J. Special Topics 173  (2009) 147-166.

214. Solitons in normally  dispersive mode-locked lasers, M.J.  Ablowitz and T.P.  Horikis, Physical

Review A 79 (2009) 063845.

215.   A reformulation and  applications of interfacial  fluids  with  a  free surface,  T.S.  Haut  and

M.J.  Ablowitz,  J. Fl.  Mech.  631  (2009) 375-396.

216.   Asymptotic expansions  for  solitary  gravity-capillary  waves  in  two  and  three  dimensions, M.J.  Ablowitz and T.S. Haut,  Proc.  Roy.  Soc.  A 465  (2009) 2725-2749

217. Soliton strings and interactions in mode-locked lasers, Mark J. Ablowitz, Theodoros  P. Horikis and Sean D. Nixon Opt.  Commun.282 (2009) 4127-4135.

218.   Coupled  nonlinear  Schr¨odinger  equations  from  interfacial  fluids with  a  free surface,  M.J.

Ablowitz and T.S. Haut,  Theor.  Math.  Phys.  159  (2009) 689-697.

219. Nonlinear  waves in optical  media,  Mark J. Ablowitz,  Theodoros  P. Horikis, Journal of Com- putational and Applied Mathematics 234  (2010) 1896-1903.

220.  Band  Gap  Boundaries  and  Fundamental Solitons  in Complex  2D Nonlinear  Lattices,  M.J.

Ablowitz,  N. Antar,  I. Bakirtas  and B. Ilan, Physical  Review A, 81 (2010) 033834.

221. Parameterizations of the Chazy Equation, S. Chakravarty and M. J. Ablowitz, Stud.  in Appl.

Math.,  124,  (2010) 105-135.

222.  Asymptotic expansions  for large  amplitude solitary  gravity-capillary waves,  M.J.  Ablowitz and T.S. Haut,  J. Phys.  Math and Theoretical, 43 (2010) 434005.

223. Evolution  of Bloch-mode-envelopes  in two-dimensional generalized  honeycomb  lattices,  Mark

J. Ablowitz,  and Yi Zhu, Physical  Review A 82 (2010) 013840.

224.   Perturbations of dark  solitons,    M.  J.  Ablowitz,  S.  D.  Nixon,  T.  P.  Horikis  and  D.  J.

Frantzeskakis, Proc.  Roy.  Soc.  A 467  (2011) 2597-2621.

*225. Nonlinear wave dynamics:  from lasers to fluids, Mark J. Ablowitz, Terry  S. Haut,  Theodoros P. Horikis, Sean D. Nixon and Yi Zhu, Discrete  and Continuous Dynamical  Systems, Series S 4 (2011) 923-955

226.  Dark  solitons  in mode-locked  lasers,  M. J.  Ablowitz,  T.  P.  Horikis,  S. D. Nixon,  and  D. J.

Frantzeskakis, Opt.  Lett.  36 (2011) 793-795

227. On the evolution  of perturbations to solutions  of the Kadomtsev-Petviashvilli equation  using the Benney-Luke  equation,  M. J. Ablowitz and W. C. Curtis,  J. Phys.  A-Math  and Theor.

44 (2011) 195202

228. Nonlinear  diffraction  in photonic  graphene,  Mark J. Ablowitz,  and Yi Zhu, Optics Letters  36

(2011) 3762-3764

229. Nonlinear waves in shallow honeycomb lattices,  M. J. Ablowitz and Yi Zhu, SIAM J. on Appl.

Math.,72, (2012) 240-260

230.  Vortex  and  dipole  solitons  in complex  2D nonlinear  lattices,  M. J.  Ablowitz,  N. Antar,   I.

Bakirtas  and B. Ilan, Phys.  Rev.  A, . 86, (2012) 033804

231.  **Nonlinear  shallow ocean-wave  soliton  interactions on flat beaches,  M. J.  Ablowitz  and  D.

E. Baldwin,  Phys.  Rev.  E, . 86 036305 (2012)

232. On tight-binding approximations in optical  lattices,  M.J.  Ablowitz,  Mark J., C.W. Curtis,  Y.

Zhu, Stud.  Appl.  Math.,129, (2012) 362-388

233.   Traveling  waves  in  elastic  rods  with  arbitrary curvature and  torsion,  M.  J.  Ablowitz,  V.

Barone,  S. De Lillo and M. Sommacal,   J. Nonlinear  Sci.22  (2012), 1013-1040

234.  Unified Orbital  Description  of the Envelope  Dynamics  in Two-Dimensional  Simple Periodic

Lattices,  M.J.  Ablowitz and Y. Zhu, Stud.  Appl.  Math,  131  (2013) 41-71

235.  Integrable  nonlocal  nonlinear  Schrodinger  equation,  M. J.  Ablowitz  and  Z. H. Musslimani,

Phys.  Rev.  Lett.  110  (2013) 064105

236.  Interactions and  asymptotics of dispersive  shock waves - Korteweg-de  Vries Equation, M. J.

Ablowitz and D. E. Baldwin,  Phys Lett.  A, 377  (2013) 555-559

237. Dark solitons of the power-energy  saturation model:  application to mode-locked lasers, M. J.

Ablowitz,  T. P. Horikis, S. D. Nixon, and D. J. Frantzeskakis, J. of Phys.  A: Math.  Theor.

46  (2013) 095201

238. Dispersive shock wave interactions and asymptotics, M. J. Ablowitz and D. E. Baldwin, Phys.

Rev.  E., 87 (2013) 022906

239.  Conservation Laws and  nondecaying-solutions for the  Benney-Luke  equation,  M.J.  Ablowitz and C.W.  Curtis,  Proc.  R. Soc.  A, 469,  (2013) 201206

240.  Localized nonlinear  edge states  in honeycomb  lattices,  M.J.  Ablowitz  and  C.W.  Curtis,  88

Phys.  Rev.  A (2013) 013850

241. Nonlinear  wave packets  in deformed honeycomb lattices,  M.J. Ablowitz and Y. Zhu, SIAM J.

Appl.  Math.  87 (2013) 19591979

242. On the Existence of Real Spectra in PT-Symmetric Honeycomb Optical Lattices,  C. W. Curtis and M. J. Ablowitz J. of Phys.  A: Math.  Theor.  47 (2014) 225205

243.  Nonlinear  Temporal-Spatial Surface Plasmon  Polaritons, M. J. Ablowitz  and S. T. J. Butler

Optics Commun  330  (2014) 49-55

244. Inverse scattering transform for 3-level coupled Maxwell Bloch equations  with inhomogeneous broadening,  S Chakravarty, B Prinari, MJ Ablowitz, Physica  D: Nonlinear  Phenomena 278, (2014) 58-78

245.  Linear  and  nonlinear  traveling  edge waves in optical  honeycomb  lattices  MJ  Ablowitz,  CW Curtis  and YP Ma Physical  Review A 90 (2014) 023813

246. Passive mode-locking under higher order effects, T.P.  Horikis and M.J. Ablowitz, J. Opt.  Soc.

Am.  B 31 (2014) 2748-2753

  247.  Integrable  discrete  PT  symmetric  model, M. J.  Ablowitz  and  Z. H. Musslimani,  Phys.  Rev.

E 90 (2014) 03291

248. Interacting nonlinear wave envelopes and rogue wave formation in deep water, Mark J. Ablowitz and Theodoros P. Horikis, {Phys. Fluids} {vol 27} (2015) 012107

249. Unveiling pseudospin and angular momentum in photonic graphene, D. Song, V. Paltoglou, S.  Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. Efremidis and Zhigang Chen, {Nature Commun.}, {vol 6} (2015)  DOI: 10.1038

250. Adiabatic dynamics of edge waves in photonic graphene,  MJ Ablowitz, CW Curtis and YP Ma, {2D Materials} {vol 2} (2015) 024001

251. Strong transmission and reflection of edge modes in bounded photonic graphene. (2015), M.J. Ablowitz and YP Ma, {Opt. Lett.} {vol 40} (2015), 4671-4674

252. Constructive and destructive perturbations of dark solitons in mode-locked lasers,
TP Horikis, MJ Ablowitz, {Journal of Optics}  {
vol 17}, (2015) 042001

253. Inverse scattering transform for the integrable nonlocal nonlinear Schr\"odinger equation, Mark J. Ablowitz and Ziad H. Musslimani, {Nonlinearity}
vol 29} (2016) 915-946

254. Conical Wave Propagation and Diffraction in 2D Hexagonally Packed Granular Lattices, C. Chong, P.G. Kevrekidis, M.J. Ablowitz, Y-P Ma, {Phys. Rev E} {
vol 93} (2016) 012909

255. Dispersive shock waves in the Kadomtsev-Petviashvili and Two Dimensional Benjamin-Ono equations, Mark J. Ablowitz, Ali Demirci, Yi-Ping Ma, {Physica D} {
vol 333} (2016) 84-98

256. Integrable nonlocal nonlinear equations, Mark J. Ablowitz and Ziad H. Musslimani, { Studies in Applied Mathematics}, {
vol 139} (2017), 7-59

257. Rogue waves in birefringent optical fibers: elliptical and isotropic fibers, Mark J Ablowitz, Theodoros P Horikis,  { J. Optics} {
vol 19} (2017), 065501

258.  Rogue waves in nonlocal media, Theodoros P. Horikis and Mark J Ablowitz,
{Phys. Rev. E} {
vol 95} (2017), 042211

259. A universal asymptotic regime in the hyperbolic nonlinear
Schr\"odinger equation, M.J. Ablowitz
Y-P Ma and I. Rumanov, {SIAM J. Appl. Math.} {
vol 77} (2017)

260. Whitham modulation theory for the Kadomtsev– Petviashvili equation,
M.J. Ablowitz, G. Biondini and Q. Wang,  {Proc. Roy. Soc. A} {
vol 473} (2017)

261. Whitham modulation theory for the two-dimensional Benjamin-Ono equation, M.J. Ablowitz, G. Biondini and Q. Wang, { Phys. Rev. E} {
vol 96} (2017) 032225

262. Tight-binding methods for general longitudinally driven photonic lattices: Edge states and solitons
M.J. Ablowitz and J.T. Cole { Phys Rev A} {
vol 96} (2017) 043868

263. Inverse scattering transform for the nonlocal nonlinear Schrödinger
equation with nonzero boundary conditions, { J. Math. Phys.} {
vol  59} (2018) 0011501

264. Whitham modulation theory for (2+1) -dimensional equations of Kadomtsev-Petviashvili type, Mark J. Ablowitz, Gino Biondini, Igor Rumanov, {J. of Phys. A: Math. Theor.}{vol  51} (2018) 215501

265. Inverse scattering transform for the nonlocal reverse space-time sine-Gordon,
sinh-Gordon nonlinear Schrodinger equations with nonzero boundary conditions,
 MJ Ablowitz, B. Feng, X-D Luo and ZH Musslimani (2017),  {Stud. Appl. Math.} {vol. 141} (2018)

266. Solitons, the Korteweg-de Vries equation with step boundary values and pseudo-embedded eigenvalues, MJ Ablowitz, X-D Luo and J.T. Cole, {J. Math Phys.} {vol. 59} (2018) 091406


Articles denoted  by * are not contained  in web of knowledge data  base.

**This  article  plus  photos/videos taken  in Nuevo  Vallarta, Mexico by  MJA  and  Venice Beach, CA,  by  DEB,  was  featured  on  the  American  Physical  Society  (APS)  web  site:   APS  synopsis; subsequently it was identified  for a special focus article  in Physics  Today–November issue.  It also was  featured  by  the  American  Meteorological  Society  (Bulletin   January.–2013) and  was  picked up  by science news services:  ‘OurAmazingPlanet’–syndicated by many  news organizations; New Scientist;  NRC  Handelsblad:  the  largest  evening  newspaper  in Netherlands;;  National (U.S.A.)  Tsunami  Hazard  Mitigation  Program, plus others...   SIAM News requested  we write  an article  appropriate for applied  mathematicians This was subsequently published  in the June, 2013 issue of SIAM News.