Hamiltonian higher-order nonlinear Schrödinger equations for broader-banded waves on deep water

European Journal of Mechanics, B/Fluids

Volumn 32, Issue 1, 2012, Pages 22-31

  Craig, Walter ^a   Guyenne, Philippe ^b   Sulem, Catherine ^c  

^a MCMASTER UNIVERSITY   (Canada)

^b UNIVERSITY OF DELAWARE   (United States)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

DirichletNeumann operator; Hamiltonian systems; Modulation theory; Nonlinear Schr dinger equation; Symplectic integrators; Water waves

Indexed keywords

DEEP WATER; DEEP-WATER WAVES; DINGER EQUATION; DIRICHLET-NEUMANN OPERATOR; HAMILTONIAN FORMULATIONS; HAMILTONIAN SYSTEMS; HIGHER ORDER; MODULATION THEORY; NEW MODEL; STABILITY ANALYSIS; STABILITY PROPERTIES; SYMPLECTIC; SYMPLECTIC INTEGRATORS; TIME-INTEGRATION SCHEME; WATER-WAVE PROBLEM;

COMPUTER SIMULATION; NONLINEAR EQUATIONS; STABILITY; WATER WAVES;

HAMILTONIANS;

EID: 84856239629     PISSN: 09977546     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechflu.2011.09.008     Document Type: Article

References (27)

1. D.U. Martin, and H.C. Yuen Quasi-recurring energy leakage in the two-space-dimensional nonlinear Schrödinger equation Phys. Fluids 23 1980 881 883
2. K.B. Dysthe Note on a modification to the nonlinear Schrödinger equation for application to deep water waves Proc. R. Soc. Lond. A 369 1979 105 114
3. U. Brinch-Nielsen, and I.G. Jonsson Fourth order evolution equations and stability analysis for Stokes waves on arbitrary water depth Wave Motion 8 1986 455 472 (Pubitemid 17463922)
4. K. Trulsen, and K.B. Dysthe A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water Wave Motion 24 1996 281 289 (Pubitemid 126321259)
5. K. Trulsen, I. Kliakhandler, K.B. Dysthe, and M.G. Velarde On weakly nonlinear modulation of waves on deep water Phys. Fluids 12 2000 2432 2437
6. J.W. McLean Instabilities of finite-amplitude water waves J. Fluid Mech. 114 1982 315 330
7. V.E. Zakharov Stability of periodic waves of finite amplitude on the surface of a deep fluid J. Appl. Mech. Tech. Phys. 9 1968 190 194
8. W. Craig, P. Guyenne, and C. Sulem A Hamiltonian approach to nonlinear modulation of surface water waves Wave Motion 47 2010 552 563
9. W. Craig, P. Guyenne, and C. Sulem Coupling between internal and surface waves Nat. Hazards 57 2011 617 642
10. O. Gramstad, and K. Trulsen Hamiltonian form of the modified nonlinear Schrödinger equation for gravity waves on arbitrary depth J. Fluid Mech. 670 2011 404 426
11. V.P. Krasitskii On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves J. Fluid Mech. 272 1994 1 20
12. W. Craig, and C. Sulem Numerical simulation of gravity waves J. Comput. Phys. 108 1993 73 83
13. L. Xu, and P. Guyenne Numerical simulation of three-dimensional nonlinear water waves J. Comput. Phys. 228 2009 8446 8466
14. R. Coifman, and Y. Meyer Nonlinear harmonic analysis and analytic dependence Proc. Sympos. Pure Math. 43 1985 71 78
15. O.M. Phillips On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions J. Fluid Mech. 9 1960 193 217
16. A. de Bouard, W. Craig, O. Daz-Espinosa, P. Guyenne, and C. Sulem Long wave expansions for water waves over random topography Nonlinearity 21 2008 2143 2178
17. W. Craig, and M.D. Groves Hamiltonian long-wave approximation to the water-wave problem Wave Motion 19 1994 367 389
18. W. Craig, P. Guyenne, J. Hammack, D. Henderson, and C. Sulem Solitary water wave interactions Phys. Fluids 18 2006 057106
19. W. Craig, P. Guyenne, D.P. Nicholls, and C. Sulem Hamiltonian long-wave expansions for water waves over a rough bottom Proc. R. Soc. Lond. A 461 2005 839 873 (Pubitemid 40522452)
20. W. Craig, P. Guyenne, and C. Sulem Water waves over a random bottom J. Fluid Mech. 640 2009 79 107
21. P. Guyenne, and D.P. Nicholls A high-order spectral method for nonlinear water waves over moving bottom topography SIAM J. Sci. Comput. 30 2007 81 101
22. W. Craig, P. Guyenne, and H. Kalisch Hamiltonian long-wave expansions for free surfaces and interfaces Commun. Pure Appl. Math. 58 2005 1587 1641 (Pubitemid 43082564)
23. W. Craig, C. Sulem, and P.-L. Sulem Nonlinear modulation of gravity waves: a rigorous approach Nonlinearity 5 1992 497 522
24. S. Leblanc Stability of bichromatic gravity waves on deep water Eur. J. Mech. B/Fluids 28 2009 605 612
25. P.A. Milewski, and E.G. Tabak A pseudospectral procedure for the solution of nonlinear wave equations with examples from free-surface flows SIAM J. Sci. Comput. 21 1999 1102 1114
26. B. Leimkuhler, and S. Reich Simulating Hamiltonian Dynamics 2004 Cambridge University Press Cambridge
27. M.S. Longuet-Higgins The instabilities of gravity waves of finite amplitude in deep water II. Subharmonics Proc. R. Soc. Lond. A 360 1978 489 505