Articles
in reverse chronological order
128. Dilaton Mass Formulas in a Hairy Binary Black Hole Model, Journal of Mathematical Physics, submitted [with S. Chen].
127. Determination of anti-de Sitter Monopole Wall via Minimization, Journal of Mathematical Physics 60 (2019) 073509 [with L. Cao].
126. Solutions to the Minimization Problem Arising in a Dark Monopole Model in Gauge Field Theory, Nuclear Physics B, in press [with X. Zhang].
125. Coexisting Vortices and Antivortices Generated by Dually Gauged Harmonic Maps, Communications in Mathematical Physics, submitted [with X. Han and G. Huang].
124. Determination of Bending Angle of Light Deflection Subject to Possible Weak and Strong Quantum Gravity Effects, Journal of Mathematical Physics, submitted [with C. Xu].
123. Domain Wall Solitons Arising in Classical Gauge Field Theories, Communications in Mathematical Physics 369 (2019) 317--349 [with L. Cao and S. Chen].
122. Integer-Squared Laws for Global Vortices in the Born–Infeld Wave Equations, Annals of Physics 400 (2019) 303–319 [with Z. Gao and S. B. Gudnason].
121. Topological Bounds of Bending Energy for Cell Vesicles, Physical Review E 97 (2018) 062409.
120. Determination of Angle of Light Deflection in Higher-Derivative Gravity Theories, Journal of Mathematical Physics 59 (2018) 032501 [with C. Xu].
119. Boundary Charges and Integral Identities in Field Theories, Nuclear Physics B, Nuclear Physics B 925 (2017) 500--535 [with S. B. Gudnason and Z. Gao].
118. Solutions of Friedmann's Equations and Cosmological Consequences, Proceedings of International Congress of Chinese Mathematicians, 2016. 19 pages. To appear.
117. Determination of Gap Solution and Critical Temperature in Doped Graphene Superconductivity, Zeitschrift fĂĽr Angewandte Mathematik und Physik 68 (2017) 34 [20 pp.] [with C. Xu].
116. Critical Pull-in Curves of MEMS Actuators in Presence of Casimir Force,
Zeitschrift fĂĽr Angewandte Mathematik und Mechanik 96 (2016) 1406--1422 [with Brenda McLellan, Luciano Medina, and Chenmei Xu].
115. Domain Wall Equations, Hessian of Superpotential, and Bogomol’nyi Bounds, Nuclear Physics B 904 (2016) 470--493 [with S. Chen].
114. Magnetic Impurity Inspired Abelian Higgs Vortices, Journal of High Energy Physics 2 (2016) 046 [with X. Han].
113. Non-Abelian Clouds Around Reissner--Nordstrom Black Holes: The Existence Line, Physical Review D 93 (2016) 124069 [with E. Radu and D. H. Tchrakian].
112. Relativistic Chern--Simons--Higgs Vortex Equations, Transactions of American Mathematical Society 368 (2016) 3565--3590 [with X. Han].
111. Resolution of Chern--Simons--Higgs Vortex Equations, Communications in Mathematical Physics 343 (2016) 701--724 [with X. Han and C. S. Lin].
110. Friedmann-Lemaitre Cosmologies via Roulettes and Other Analytic Methods, Journal of Cosmology and Astroparticle Physics 10 (2015) 056 [with S. Chen and G. W. Gibbons].
109. Topologically Stratified Energy Minimizers in a Product Abelian Field Theory, Nuclear Physics B 898 (2015) 605--626 [with X. Han].
108. Explicit Integration of Friedmann's Equation with Nonlinear Equations of State, Journal of Cosmology and Astroparticle Physics 05 (2015) 020 [with S. Chen and G. W. Gibbons].
107. Existence of Hyperbolic Calorons, Proceedings of the Royal Society (London) Series A 471 (2015) 2176 [with L. Sibner and R. Sibner].
106. Existence Theorems for Vortices in the Aharony--Bergman--Jaferis--Maldacena Model, Communications in Mathematical Physics 333 (2015) 229--259 [with X. Han].
105. Friedmann's Equations and Chebyshev's Theorem, Journal of Cosmology and Astroparticle Physics, 12 (2014) 035 [with S. Chen, G. W. Gibbons, and Y. Li].
104. Cosmic Strings in a Product Abelian Gauge Field Theory, Nuclear Physics B 885 (2014) 25--33.
103. Exact Kink Solitons in Skyrme Crystals, Physical Review D 89 (2014) 025007 [with S. Chen and Y. Li].
102. Chern--Simons Vortices in the Gudnason Model, Journal of Functional Analysis 267 (2014) 678--726 [with X. Han, C. S. Lin, and G. Tarantello].
101. Existence of Optical Vortices, SIAM Journal of Mathematical Analysis 46 (2014) 484--498 [with R. Zhang].
100. Knots in Field Theory and Universal Topological Growth Laws, Proceedings of International Congress of Chinese Mathematicians, 2013. 14 pages.
99. Abelian Hopfions of the $CP^n$ Model on $R^{2n+1}$ and a Fractionally Powered Topological Lower Bound, Nuclear Physics B 875 (2013) 388--407 [with E. Radu and D. H. Tchrakian].
98. Solutions to the Master Equations Governing Fractional Vortices, Journal of Differential Equations 254 (2013) 1437--1463 [with C. S. Lin and G. Tarantello].
97. Exact Kink Solitons in a Monopole Confinement Problem, Physical Review D 86 (2012) 085030 [with S. X. Chen and Y. Li].
96. Existence of Multiple Vortices in Supersymmetric Gauge Field Theory,
Proceedings of Royal Society (London) A 468 (2012) 3923--3946 [with S. X. Chen].
95. Existence of Dyons in Minimally Gauged Skyrme Model via Constrained Minimization, Journal of Functional Analysis 262 (2012) 3602--3625 [with Z. F. Gao].
94. Non-Abelian Vortices in Supersymmetric Gauge Field Theory via Direct Methods, Communications in Mathematical Physics 313 (2012) 445--478 [with Elliott H. Lieb].
93. Sharp Existence and Uniqueness Theorems for
Non-Abelian Multiple Vortex Solutions, Nuclear Physics B 846 (2011) 650--676 [with C. S. Lin].
92. Dynamics of Electrostatic MEMS Actuators, Journal of Mathematical Physics 53 (2012) 022703 [with R. Zhang and L. Zhao].
91. Electrically Charged Solitons in Gauge Field Theory, Acta Mathematica Scientia (invited survey article dedicated to the memory of Guoping Li and Xinmou Wu) 30 (2010) 1975--2005.
90. On a Vegetation Pattern Formation Model Governed by a Nonlinear Parabolic System, Nonlinear Analysis 14 (2013) 507--525 [with Kaloyan Marinov and Tianze Wang].
89. Existence of Dyons in the Coupled Georgi--Glashow--Skyrme Model, Annales de Henri Poincare 12 (2011) 329--349 [with Fanghua Lin].
88. Non-Abelian Multiple Vortices in Supersymmetric Field Theory, Communications in Mathematical Physics 304 (2011) 433--457 [with Chang-Shou Lin].
87. Charged Cosmological Dust Solutions of the Coupled Einstein and Maxwell Equations, Discrete and Continuous Dynamical Systems (in honor of Louis Nirenberg) 28 (2010) 567--589 [with Joel Spruck].
86. Phase Transition Solutions in Geometrically Constrained Magnetic Domain Wall Models, Journal of Mathematical Physics 51 (2010) 023504 [with S. X. Chen].
85. Proof of the Julia--Zee Theorem, Communications in Mathematical Physics 291 (2009) 347--356 [with Joel Spruck].
84. Electrically and Magnetically Charged Vortices in the Chern-Simons-Higgs Theory, Proceedings of the Royal Society (London) A 465 (2009) 3489--3516 [with R. Chen, Y. Guo, and D. Spirn].
83. Steady State Solutions for Nonlinear Schroedinger Equation Arising in Optics, Journal of Mathematical Physics 50 (2009) 053501 [with R. F. Zhang] [Corrigendum]. (This article was one of the top 20 most downloaded articles in the months of May and June, 2009, of the journal.)
82. Existence of Faddeev Knots in General Hopf Dimensions, Surveys in Differential Geometry 13 (2009) 149--221 [with F. B. Hang and F. H. Lin].
81. Universal Growth Law for Knot Energy of Faddeev Type in General Dimensions, Proceedings of the Royal Society A 646 (2008) 2741--2757 [with F. H. Lin].
80. Existence of Knots of Minimum Energy and Topological Growth Laws in the Faddeev Model, Topology and Physics (in memory of Xiao-Song Lin), Nankai Tracts in Mathematics12 (2008) pp. 242--259 [with F. H. Lin].
79. Spherically Symmetric Self-Dual Yang-Mills Instantons on Curved Backgrounds in All Even Dimensions, Physical Review D 77 (2008) 044017 [with E. Radu and D. H. Tchrakian].
78. A System of Elliptic Equations Arising in Chern-Simons Field Theory, Journal of Functional Analysis 247 (2007) 289--350 [with C. S. Lin and A. C. Ponce].
77. Analysis on Faddeev Knots and Skyrme Solitons: Recent Progress and Open Problems, in Perspectives in Nonlinear Partial Differential Equations (in honor of Haim Brezis), Contemporary Mathematics 446, pp. 319--344, American Mathematical Society, 2007 [with F. H. Lin].
76. Geometry, Topology, and Gravitation Synthesized by Cosmic Strings, Pure and Applied Mathematics Quarterly 3 (2007) 737--772 (in honor of Robert Gulliver, Robert Hardt, and Leon Simon).
75. Generalized Bernstein Property and Gravitational Strings in Born--Infeld Theory, Nonlinearity 20 (2007) 1193--1213 [with L. Sibner and R. Sibner].
74. Nonlinear Nonlocal Elliptic Equations Modeling Electrostatic Actuation, Proceedings of the Royal Society A 463 (2007) 1323--1337 [with F. H. Lin].
73. Energy Splitting, Substantial Inequality, and Minimization for the Faddeev and Skyrme Models, Communications in Mathematical Physics 269 (2007) 137--152 [with F. H. Lin].
72. Moduli Space of BPS Walls in Supersymmetric Gauge Theories, Communications in Mathematical Physics 267 (2006) 783--800 [with N. Sakai].
71. Static Knot Energy, Hopf Charge, and Universal Growth Law, Nuclear Physics B 747 (2006) 455--463 [with F. H. Lin].
70. Faddeev Knots, Skyrme Solitons, and Concentration-Compactness, Proceedings of the 23rd International Conference on Differential Geometry Methods in Theoretical Physics, Nankai Tracts in Mathematics 10 (2006) pp. 313--322 [with F. H. Lin].
69. Existence of Static BPS Monopoles and Dyons in Arbitrary $(4p-1)$-Dimensional Spaces, Letters in Mathematical Physics 77 (2006) 249--263 [with X. Q. Wang].
68. Mathematical Analysis of the Multiband BCS Gap Equations in Superconductivity, Physica D 200 (2005) 60--74.
67. Existence of 2D Skyrmions via Concentration-Compactness Method, Communications on Pure and Applied Mathematics 57 (2004) 1332--1351 [with F. H. Lin].
66. Prescribing Zeros and Poles on a Compact Riemann Surface for a Gravitationally Coupled Abelian Gauge Field Theory, Communications in Mathematical Physics 249 (2004) 579--609.
65. Existence of Energy Minimizers as Stable Knotted Solitons in the Faddeev Model, Communications in Mathematical Physics 249 (2004) 273--303 [with F. H. Lin].
64. The Faddeev Knots as Stable Solitons: Existence Theorems, Science in China Series A 47 (2004) 187--197 [with F. H. Lin].
63. Gauged Harmonic Maps, Born--Infeld Electromagnetism, and Magnetic Vortices,Communications on Pure and Applied Mathematics 56 (2003) 1635--1665 [with F. H. Lin].
62. On Pokrovskii's Anisotropic Gap Equations in Superconductivity Theory, Nonlinearity 16 (2003) 2061--2073.
61. Rigorous Proof of Isotope Effect by Bardeen--Cooper--Schrieffer Theory, Journal of Mathematical Physics 44 (2003) 2004--2025.
60. Multiple Instantons Representing Higher-Order Chern--Pontryagin Classes, II, Communications in Mathematical Physics 241 (2003) 47--67 [with L. Sibner and R. Sibner].
59. Existence of Solutions to the Efros Self-consistency Equation in All Dimensions,Proceedings of the Royal Society A 459 (2003) 853--861.
58. The Uniqueness and Approximation of a Positive Solution of the Bardeen--Cooper--Schrieffer Gap Equation, Journal of Mathematical Physics 41 (2000) 6007--6025 [with J. B. McLeod].
57. Classical Solutions in the Born--Infeld Theory, Proceedings of the Royal Society A 456 (2000) 615--640.
56. Abelian Gauge Theory on Riemann Surfaces and New Topological Invariants, Proceedings of the Royal Society A 456 (2000) 593--613 [with R. Sibner and L. Sibner].
55. On a System of Nonlinear Elliptic Equations Arising in Theoretical Physics, Journal of Functional Analysis 170 (2000) 1--36.
54. Strings of Opposite Magnetic Charges in a Gauge Field Theory, Proceedings of the Royal Society A 455 (1999) 601--629.
53. Sigma Models Coupled with Abelian Gauge Fields, Journal of Mathematical Physics 39 (1998) 5824--5831 [with D. O'Keeffe and D. H. Tchrakian].
52. Chern--Simons Solitons and a Nonlinear Elliptic Equation, Helvetica Physica Acta 71 (1998) 573--585.
51. Coexistence of Vortices and Anti-vortices in an Abelian Gauge Theory, Physical Review Letters 80 (1998) 26--29.
50. String-like Defects and Fractional Total Curvature in a Gauged Harmonic Map Model, Advances in Nonlinear Partial Differential Equations and Related Areas (edited by Y. Li et al), pp. 334--378, World Scientific Publishing, 1998.
49. The Lee--Weinberg Magnetic Monopole of Unit Charge: Existence and Uniqueness, Physica D 117 (1998) 215--240.
48. Dually Charged Particle-like Solutions in the Weinberg--Salam Theory, Proceedings of the Royal Society A 454 (1998) 155--178.
47. Nonlinear Problems in Field Theories, Proceedings of International Workshop on Mathematical and Physical Aspects of Nonlinear Field Theories, Lecture Notes Series 42, pp. 1--26, 1998, Seoul National University (edited by D. Chae).
46. Multiple Instantons Representing Higher-Order Chern--Pontryagin Classes, Communications in Mathematical Physics 188 (1997) 737--751 [with J. Spruck and D. H. Tchrakian].
45. The Relativistic Non-Abelian Chern--Simons Equations, Communications in Mathematical Physics 186 (1997) 199--218.
44. The Existence of Solitons in Gauged Sigma Models with Broken Symmetry: Some Remarks, Letters in Mathematical Physics 40 (1997) 177--189.
43. Topological Solitons in the Weinberg--Salam Theory, Physica D 101 (1997) 55--94.
42. Cosmic Strings on $S^2$ and Criticality, Proceedings of the Royal Society A 453 (1997) 581--591.
41. A Necessary and Sufficient Condition for the Existence of Multisolitons in a Self-Dual Sigma Model, Communications in Mathematical Physics 181 (1996) 485--506.
40. Topological and Nontopological Self-Dual Chern--Simons Solitons in a Gauged $O(3)$ Sigma Model, Physical Reviews D 54 (1996) 5245--5258 [with K. Arthur and D. H. Tchrakian].
39. Mathematical Theory of Self-Dual Cosmic Strings: Existence and Obstructions, International Journal of Modern Physics A 11 (1996) 203--227 [invited review article].
38. Skyrme Models with Self-Dual Limits: $d=2,3$, Journal of Mathematical Physics 37 (1996) 2569--2584 [with K. Arthur, G. Roche, and D. H. Tchrakian].
37. The Existence of Generalised Self-Dual Chern--Simons Vortices, Letters in Mathematical Physics 36 (1996) 403--413 [with D. H. Tchrakian].
36. Existence Theorems for Periodic Non-relativistic Maxwell--Chern--Simons Solitons, Journal of Differential Equations 127 (1996) 571--589 [with J. Spruck].
35. Prescribing Topological Defects for the Coupled Einstein and Abelian Higgs Equations, Communications in Mathematical Physics 170 (1995) 541--582.
34. Regular Stationary Solutions of the Cylindrically Symmetric Einstein-Matter-Gauge Equations, Journal of Mathematical Analysis and Applications 195 (1995) 160--190 [with J. Spruck].
33. Vortex Condensation in the Chern--Simons Higgs Model: An Existence Theorem,Communications in Mathematical Physics 168 (1995) 321--336 [with L. A. Caffarelli].
32. Topological Solutions in the Self-Dual Chern--Simons Theory: Existence and Approximation, Annales de l'Institut Henri Poincar\'{e}-- Analyse non Lin\'{e}aire 12 (1995) 75--97 [with J. Spruck].
31. The Existence of Ginzburg--Landau Solution on the Plane by a Direct Variational Method, Annales de l'Institut Henri Poincar\'{e} -- Analyse non Lin\'{e}aire 11 (1994) 517--536.
30. Obstructions to the Existence of Static Cosmic Strings in an Abelian Higgs Model, Physical Review Letters 72 (1994) 10--13.
29. Self Duality of the Gauge Field Equations and the Cosmological Constant, Communications in Mathematical Physics 162 (1994) 481--498.
28. A Nonlinear Elliptic Equation Arising from Gauge Field Theory and Cosmology,Proceedings of the Royal Society A 446 (1994) 453--478 [with X. Chen, S. Hastings, and J. B. McLeod].
27. The Critical Temperature and Gap Solution in the Bardeen--Cooper--Schrieffer Theory of Superconductivity, Letters in Mathematical Physics 29 (1993) 133--150 [with Q. Du].
26. An Equivalence Theorem for String Solutions of the Einstein-Matter-Gauge Equations, Letters in Mathematical Physics 26 (1992) 79--90.
25. On the Existence of Multivortices in a Generalized Bogomol'nyi System, Zeitschrift f\"{u}r angewandte Mathematik und Physik 43 (1992) 677--696.
24. The Existence of a Class of Cosmic String Solutions with Infinite Energy, Proceedings of the Royal Society of Edinburgh A 122 (1992) 301--315.
23. The Existence of Non-Topological Solitons in the Self-Dual Chern--Simons Theory, Communications in Mathematical Physics 149 (1992) 361--376 [with J. Spruck].
22. On Multivortices in the Electroweak Theory. I: Existence of Periodic Solutions, Communications in Mathematical Physics 144 (1992) 1--16 [with J. Spruck].
21. On Multivortices in the Electroweak Theory. II: Existence of Bogomol'nyi Solutions in ${\bf R}^2$, Communications in Mathematical Physics 144 (1992) 215--234 [with J. Spruck].
20. Symmetric Superconducting States in Thin Films, SIAM Journal on Applied Mathematics52 (1992) 614--629 [with S. Wang].
19. Abrikosov's Vortices in the Critical Coupling, SIAM Journal on Mathematical Analysis 23 (1992) 1125--1140 [with S. Wang].
18. Solutions of the Generalized Bogomol'nyi Equations via Monotone Iterations, Journal of Mathematical Physics 33 (1992) 4239--4249 [with S. Wang].
17. Vacuum Decay of Non-Abelian Vortices, Mathematical Methods in the Applied Sciences15 (1992) 79--88.
16. A Generalized Self-Dual Chern--Simons Higgs Theory, Letters in Mathematical Physics 23 (1991) 179--191.
15. Existence of the Massive $SO(3)$ Vortices, Journal of Mathematical Physics 32 (1991) 1395--1399.
14. On the Bardeen--Cooper--Schrieffer Integral Equation in the Theory of Superconductivity, Letters in Mathematical Physics 22 (1991) 27--37.
13. On the Abelian Higgs Models with Sources, Journal de Math\'{e}matiques Pures et Appliqu\'{e}es 70 (1991) 325--344.
12. The Computation of Superconductivity in Thin Films, Journal of Computational Physics89 (1990) 257--275 [with S.-Y. Lin].
11. Vortices on Asymptotically Euclidean Riemann Surfaces, Nonlinear Analysis 15 (1990) 577--596.
10. Self-Dual Monopoles in a Seven-Dimensional Gauge Theory, Letters in Mathematical Physics 20 (1990) 285--290.
9. Blow-Up of the $SU(2,\bf{C})$ Yang--Mills Fields, Journal of Mathematical Physics 31 (1990) 1237--1239.
8. Ginzburg--Landau Equations for Superconducting Films and the Meissner Effect, Journal of Mathematical Physics 31 (1990) 1284--1289.
7. Boundary Value Problems of the Ginzburg--Landau Equations, Proceedings of the Royal Society of Edinburgh A 114 (1990) 355--365.
6. Convergence of the Pseudospectral Method for the Ginzburg--Landau Equation, Journal of Mathematical Analysis and Applications 147 (1990) 556--568.
5. Existence of Solutions for a Generalized Yang--Mills Theory, Letters in Mathematical Physics 19 (1990) 257--267.
4. On the Ginzburg--Landau Wave Equation, Bulletin of the London Mathematical Society 22 (1990) 167--170.
3. A Comparison of the Eigenvalues of Two Sturm--Liouville Problems, Canadian Mathematical Bulletin 33 (1990) 386--390.
2. Existence, Regularity, and Asymptotic Behavior of the Ginzburg--Landau Equations on ${\bf R}^3$, Communications in Mathematical Physics 123 (1989) 147--161.
1. Generalized Skyrme Models on Higher Dimensional Riemannian Manifolds, Journal of Mathematical Physics 30 (1989) 824--828.