Publications - Preprints

"Nearly everything is really interesting if you go into it deeply enough"

Richard Feynman

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Papers in Refereed Journals

1. The complex-step Newton method and its convergence (PDF) (Appendix)

2. Mechanical balance laws for two-dimensional Boussinesq systems (with C. Hassanieh, S. Israwi, H. Kalisch and A. Senthilkumar) (PDF)

3. On the well-posedness of the Galerkin semidiscretization of the periodic initial-value problem of the Serre equations (with D. Antonopoulos and V. Dougalis) (PDF)

4. Bona-Smith-type systems in bounded domains with slip-wall boundary conditions: Theoretical justification and a conservative numerical scheme, Journal of Scientific Computing 102(2025) DOI:10.1007/s10915-024-02742-8 (PDF)

5. On the lifespan of nonzero background solutions to a class of focusing nonlinear Schrodinger equations, (with D. Hennig, N. Karachalios and D. Mantzavions), Wave Motion 132(2025), 103419, DOI:10.1016/j.wavemoti.2024.10341 (PDF)

6. Oscillatory and regularized shock waves for a modified Serre-Green-Naghdi system, (with D. Bolbot and A. Tzavaras), Studies in Applied Mathematics, 153(2024), e12694, DOI:10.1111/sapm.12694 (PDF)

7. On iterative methods based on Sherman-Morrison-Woodbury splitting, Applied Numerical Mathematics, 201(2024), 282-289, DOI: 10.1016/j.apnum.2024.3.007 (PDF) (Appendix)

8. Oscillatory and regularized shock waves for a dissipative Peregrine-Boussinesq system, (with L. Brudvik-Lindner and A. Tzavaras), IMA Journal of Applied Mathematics, 88(2023), 602-631, DOI: 10.1093/imamat/hxad030  (PDF)

9. Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. II. Dynamics (with J. Bona and A. Duran), Water Waves, 5(2023), 161-190, DOI: 10.1007/s42286-023-00076-w (PDF)

10. Equations for small amplitude shallow water waves over small bathymetric variations, (S. Israwi and Y. Khalifeh), Proc. R. Soc. A, 479(2023),  20230191, DOI: 10.1098/rspa.2023.0191 (PDF with corrections)

11. Dispersive shocks in diffusive-dispersive approximations of elasticity and quantum-hydrodynamics, (with D. Bolbot and A. Tzavaras) Quart. Appl. Math. 81(2023), 455-481, DOI: 10.1090/qam/1658   (PDF)

12. Extended water wave systems of Boussinesq equations on a finite interval: Theory and numerical analysis, (with D. Mantzavinos), Journal de Mathématiques Pures et Appliquées, 169(2023), 109-137,  DOI: 10.1016/j.matpur.2022.11.009 (PDF)

13. Deep learning of inverse water waves problems using multi-fidelity data:  Application to Serre-Green-Naghdi equations (with A. Jagdap and G. Karniadakis) Ocean Engineering, 248(2022), 110775, DOI:10.1016/j.oceaneng.2022.110775 (PDF)

14. A regularized shallow-water waves system with slip-wall boundary conditions in a basin: Theory and numerical analysis (with S. Israwi, H. Kalisch and T. Katsaounis) Nonlinearity, 35(2022), 750-786, DOI:10.1088/1361-6544/ac3c29 (PDF)

15.  A conservative fully-discrete numerical method for the regularised shallow water wave equations (with D. Ketcheson, H. Ranocha and E. Süli) SIAM J. Sci. Comput. 43(2021), B508-B537, DOI: 10.1137/20M1364606 (PDF)

16. A broad class of conservative numerical methods for dispersive wave equations (with H. Ranocha and D. Ketcheson) Commun. Comput. Phys. 29(2021), 979-1029, DOI:10.402/cicp.OA-2020-0119 (PDF)

17. Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. Approximations (with J. Bona and A. Duran), Discrete Contin. Dyn. Syst. 41(2021), 87-111,  DOI: 10.3934/dcds.2020215 (PDF)

18. Boussinesq-Peregrine water wave models and their numerical approximation (with Th. Katsaounis and G. Sadaka), J. Comp. Phys. 417 (2020), 109579, DOI:10.1016/j.jcp.2020.109579 (PDF)

19. Hamiltonian regularisation of shallow water equations with uneven bottom (with D. Dutykh and D. Clamond), J. Phys. A: Math. Theor.  52 (2019) 42LT01, DOI: 10.1088/1751-8121/ab3eb2 (PDF)

20. Error estimates for Galerkin finite element methods for the Camassa-Holm equation (with D. Antonopoulos and V. Dougalis), Numerische Mathematik 142(2019), 833-862, DOI: 10.1007/s00211-019-01045-7 (PDF)

21. On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization (with A. Duran and D. Dutykh), Physica D 397(2019), 1-16,  DOI: 10.1016/j.physd.2019.05.002 (PDF)

22. On some model equations for pulsatile flow in viscoelastic vessels (with D. Dutykh, Q. Li and E. Peach), Wave Motion 90(2019),139-151, DOI: 10.1016/k.wavmoti.2019.05.004 (PDF)

23. Numerical simulation of conservation laws with moving grid nodes: Application to tsunami wave modelling (with D. Dutykh, G. Khakimzyanov and N. Shokina), Geosciences 9(2019), 197, DOI: 10.3390/geosciences9050197  (PDF)

24. On the multi-symplectic structure of Boussinesq-type systems. I: Derivation and mathematical properties (with A. Duran and D. Dutykh), Physica D, 338(2019), 10-21, DOI: 10.1016/j.physd.2018.11.007 (PDF)

25. Numerical approximation to Benjamin type equations. Generation and stability of solitary waves (with A. Duran and V. Dougalis), Wave Motion, 85(2019), 34-56, DOI: 10.1016/j.wavemoti.2018.11.002  (PDF)

26. Asymptotic nonlinear and dispersive pulsatile flow in elastic vessels with cylindrical symmetry (with D. Dutykh and Q. Li), Computers and Mathematics with Applications, 75(2018), 4022-4047, DOI: 10.1016/j.camwa.2018.03.011 (PDF)

27. Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations, (with D. Dutykh and M. Hoefer), Theor. Comp. Fluid. Dyn., 32(2018), 371-397, DOI: 10.1007/s00162-018-0455-3 (PDF)

28. Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space. (with D. Dutykh, Z. Fedotova and  G. Khakimzyanov) Commun. Comput. Phys, 23(2018), 1-29, DOI: 10.4208/cicp.OA-2016-0179a (PDF)

29. On the reflection of solitons of the cubic nonlinear Schrodinger equation. (with T. Katsaounis), Math. Meth. Appl. Sci., 41(2018), 1013-1018, DOI: 10.1002/mma.4070 (PDF)

30. Error estimates for Galerkin approximations of the Serre equations. (with D. Antonopoulos and V. Dougalis), SIAM J. Numer. Anal. 55(2017), 841-868, DOI: 10.1137/16M1078355 (PDF) 

31. On weakly singular and fully nonlinear travelling shallow capillary-gravity waves in the critical regime. (with D. Dutykh, A. Assylbekuly, D. Zhakebaev), Phys. Letters A. 381(2017), 1719-1726, DOI: 10.1016/j.physleta.2017.03.041 (PDF)

32. On the nonlinear dynamics of the traveling-wave solutions of the Serre equations. (with J. Carter and D. Dutykh), Wave Motion 70(2017), 166-182, DOI: 10.1016/j.wavemoti.2016.09.008 (PDF)

33. A Modified Galerkin / Finite Element Method for the numerical solution of the Serre-Green-Naghdi system. (with M. McGuinness and C. Synolakis), Int. J. Numer. Meth. Fluids, 83(2017), 755-778, DOI: 10.1002/fld.4293 (PDF)

34. Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristics. (with D. Clamond and D. Dutykh), Commun Nonlinear Sci Numer Simulat, 45(2017) 245-257, DOI: 10.1016/j.cnsns.2016.10.009 (PDF)

35. Legendre pseudospectral approximation of Boussinesq systems and applications to wave breaking. (with M. Bjorkavag, H. Kalisch, Z. Khorsand), J. Math. Study, 49(2016), 221-237, DOI: 10.4208/jms.v49n3.16.01 (PDF)

36. Mechanical balance laws for fully nonlinear and weakly dispersive water waves. (with H. Kalisch and Z. Korshand), Physica D, 333(2016), 243-253, DOI: 10.1016/j.physd.2016.03.001 (PDF)

37. A new run-up algorithm based on local high-order analytic expansions. (with D. Dutykh, G. Khakimzyanov and N. Shokina), J. Comp. Appl. Math. 298(2016), 82-96, DOI: 10.1016/j.cam.2015.12.004 (PDF)

38. Numerical approximation of solitary waves of the Benjamin equation. (with V. Dougalis and A. Duran), Math. Comp. Simul. 127(2016), 56-79, DOI: 10.1016/j.matcom.2012.07.008 (PDF)

39. Numerical solution of the Benjamin equation. (with V. Dougalis and A. Duran), Wave Motion 52(2015), 194-215, DOI: 10.1016/j.wavemoti.2014.004 (PDF)

40. On the Galerkin/finite element method for the Serre equations. (with D. Dutykh and B. Ilan), J. Sci. Comp. 61(2014), 166-195, DOI: 10.1007/s10915-014-9823-3 (PDF)

41. On the Galilean invariance of some dispersive wave equations. (with A. Duran and D. Dutykh), Studies in Applied Mathematics, 131(2013), 359-388, DOI: 10.1111/sapm.12015  (PDF)

42. Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations. (with D. Dutykh, D. Clamond and P. Milewski), European J. Appl. Math., 24(2013), 761-787, DOI: http://dx.doi.org/10.1017/S0956792513000168 (PDF)

43. On the use of finite fault solution for tsunami generation problems. (with F. Dias, D. Dutykh and X. Gardeil), Theor. Comp. Fluid Dyn., 27(2013), 177-199, DOI: 10.1007/s00162-011-0252-8(PDF)

44. Finite volume methods for unidirectional dispersive wave models. (with D. Dutykh and T. Katsaounis), Int. J. Numer. Meth. Fluids, 71(2013), 717-736, DOI: 10.1002/fld.3681 (PDF)

45. On the contribution of the horizontal sea-bed displacements into the tsunami generation process. (with D. Dutykh L. Chubarov and Yu. Shokin), Ocean Modeling, 56(2012), 43-56, DOI: 10.1016/j.ocemod.2012.07.002 (PDF)

46. Long wave runup on random beaches. (with D. Dutykh and C. Labart), Phys. Rev. Lett., 170(2011), 184504, DOI: 10.1103/PhysRevLett.107.184504 (PDF)

47. Finite volume schemes for dispersive wave propagation and run-up (with D. Dutykh and T. Katsaounis), Journal of Computational Physics, 230(2011), 3035-3061, DOI: 10.1016/j.jcp.2011.01.003 (PDF)

48. Galerkin approximations of periodic solutions of Boussinesq systems. (with D. Antonopoulos and V. Dougalis), Bulletin of the Greek Mathematical Society, 57(2010), 13-30, hellenic mathematical society  (PDF)

49. Initial-boundary-value problems for Boussinesq systems of Bona-Smith type on a plain domain: theory and numerical analysis, (with V. Dougalis and J.-C. Saut), J. Sci. Comput. 44(2010), 109-135, DOI: 10.1007/s10915-010-9368-z (PDF)

50. On the relevance of the dam break problem in the context of nonlinear shallow water equations. (with D. Dutykh), Discrete Contin. Dyn. Syst., 13(2010), 799-818, DOI: 10.3934/dcdsb.2010.13.799 (PDF) 

51. Numerical solution of Boussinesq systems of the Bona-Smith family. (with D. Antonopoulos and V. Dougalis), Appl. Numer. Math., 30(2010), 314-336, DOI:10.1016/j.apnum.2009.03.002 (PDF). (The Appendix in (PDF))

52. Boussinesq systems in two space dimensions over a variable bottom for the generation and propagation of tsunami waves, Mat. Comp. Simul., 80(2009), 860-873,  DOI:10.1016/j.matcom.2009.08.029 (PDF)

53. On initial-boundary value problems for a Boussinesq system of BBM-BBM type in a plane domain. (with V. Dougalis and J.-C. Saut), Discrete Contin. Dyn. Syst, 23(2009), 1191–1204,  DOI:10.3934/dcds.2009.23.1191 (PDF)

54. Initial-boundary value problems for the Bona-Smith family of Boussinesq systems. (with D. Antonopoulos and V. Dougalis),  Adv. Differential Equations, 14(2009), 27–53,  1171.35457 (PDF) - Correction (PDF)

55. Numerical solution of KdV-KdV systems of Boussinesq equations: II. Generation and evolution of radiating solitary waves. (with J. Bona and V. Dougalis), Nonlinearity, 21(2008), 2825–2848,  DOI:10.1088/0951-7715/21/12/006 (PDF)

56. On some Boussinesq systems in two space dimensions: Theory and numerical analysis,  (with V. Dougalis and J.-C. Saut), Math. Model. Num. Anal., 41(2007), 825–854, DOI: 10.1051/m2an:2007043 (PDF)

57. Numerical solution of KdV-KdV systems of Boussinesq equations: I. The numerical scheme and generalized solitary waves,  (with J. Bona and V. Dougalis), Mat. Comp. Simul., 74(2007), 214–228,  DOI:10.1016/j.matcom.2006.10.004 (PDF)

58. A numerical study of the stability of solitary waves of the Bona-Smith family of Boussinesq systems,  (with V.  Dougalis, A. Duran, M. A. Lopez-Marcos), J. Nonlinear Sci., 17(2007), 569–607,  DOI:10.1007/s00332-007-9004-8 (PDF) 

Papers in Proceedings

1. Adaptive modelling of shallow fully nonlinear gravity waves. (with D. Clamond and D. Dutykh), RIMS Kokyoroku, 1947(2015), 45-65, (PDF)

2. Dispersive waves generated by an underwater landslide. Numerical methods for Hyperbolic Equations, (with D. Dutykh, S. Beysel, N. Shokina). Eds: Vazquez-Cendon et al., Taylor & Francis Group, London, pp. 245 - 250, 2013, (PDF)

3. On waves generated by an underwater landslide (with D. Dutykh, S. Beisel, N. Shokina). In Proceedings of the IV Conference "Applied Problems of the fluid mechanics, heat and mass transfer" 1-3 November 2012, Dnepropetrovsk, Ukraine, pp. 75-79, 2012,

4. Dispersive wave runup on non-uniform shores(with D. Dutykh and T. Katsaounis), Finite volumes for complex application VI - Problems & Perspectives. Springer Proceedings in Mathematics, 2011, Volume 4, Part 1, 389 - 397, (PDF)

5. Finite volume schemes for Boussinesq type equations (with D. Dutykh, T. Katsaounis), Proceedings of Colloque EDP-Normandie, 28 & 29 October 2010, Caen, France, pp. 21-28, (PDF)

6. Solitary waves of the Bona-Smith system (with V. Dougalis), Advances in scattering theory and biomedical engineering, World Scientific, New Jersey, (2004), pp. 286–294, (eds. D. Fotiadis and C. Massalas). DOI:10.1142/9789812702593_0030 (PDF) 

Books

1. Computational Mathematics: An Introduction to Numerical Analysis and Scientific Computing with Python, Chapman and Hall/CRC New York, 2023, DOI: 10.1201/9781003287292 

2. Variational Approach to Water Wave Modeling (with D. Clamond and D. Dutykh), IAHR WATER  MONOGRAPHS, International Association for Hydro-Environment Engineering  and Research (IAHR), Spain, 2024, DOI:10.3850/978-90-833476-6-0_IAHR_Watermonograph_003

Book Chapters 

1. Peregrine's system revisited. (with A. Duran and D. Dutykh), in Nonlinear Physics: fluid mechanics, nonlinear waves, hydrodynamic instabilities, pattern formation, N. Abcha, E. Pelinovsky, I. Mutabazi, Springer-Verlag, Heidelberg, 2018, pp. 3-43, DOI: 10.1007/978-3-319-78193-8_1 (PDF)

2. Theory and numerical analysis of Boussinesq systems: A review. (with V. Dougalis), in Effective Computational Methods in Wave Propagation, N. A. Kampanis, V. A. Dougalis, J. A. Ekaterinaris (eds.), CRC Press 2008, pp. 63–110,  DOI:10.1201/9781420010879.ch3  (PDF)

Technical Reports & Reviews    

1. Notes on the numerical solution of the Benjamin equation (with V. Dougalis and A. Duran) (PDF)

2. High order Discontinuous Galerkin methods and fast solution of the one dimensional scalar BBM-KdV equation near the zero dispersion limit. (with Jean-Baptiste Apoung Kamga) (PDF)

3. A simplified introduction to water waves (PDF)

4. Numerical Solution of Partial Differential Equations (with. E. Fergadakis, Dr. Th. Katsaounis), University of Crete, 1998 (in Greek)

5.  Visualisation of 2D and 3D Discrete Element Models using OpenGL and MPI. The University of Edinburgh, 2000

6. The Diameter of the Banach-Mazur Compactum, University of Crete, 2000 (B.Sc. thesis)

7. Solitary Waves of the Bona-Smith systems: Existence, Uniqueness and Stability, University of Athens, 2003 (M.Sc. Thesis)

8. Theory and numerical analysis of nonlinear and dispersive wave equations: Boussinesq systems in one and two space dimensions. University of Athens, 2007 DOI:10.12681/eadd/17161 (PhD Thesis)