A New Integrable Shallow Water Equation

Advances in Applied Mechanics

Volumn 31, Issue C, 1994, Pages 1-33

  Camassa, Roberto ^a   Holm, Darryl D ^a   Hyman, James M ^a  

^a CENTER FOR NONLINEAR STUDIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 56349110516     PISSN: 00652156     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0065-2156(08)70254-0     Document Type: Article

References (21)

1. Abarbanel, H.D. I., Holm, D.D., Phys. Fluids 30 (1985), 3369-3382
2. Ablowitz, M.J., Segur, H., Solitons and the inverse scattering transform., 1981, SIAM, Philadelphia
3. Bazdenko, S.V., Morozov, N.N., Pogutse, O.P., Sov. Phys. Dokl. 32 (1987), 262-266
4. Benjamin, T.B., Bona, J.L., Mahoney, J.J., Model equations for long waves in nonlinear dispersive systems. Phil. Trans. R. Soc. Lond. A 227 (1972), 47-78
5. Camassa, R., Holm, D.D., Dispersive barotropic equations for stratified mesoscale ocean dynamics. Physica D 60 (1992), 1-15
6. Camassa, R., Holm, D.D., A completely integrable dispersive shallow water equation with peaked solitons. Phys. Rev. Lett. 71 (1993), 1661-1664
7. Camassa, R., Wu, T.Y., Stability of forced steady solitary waves. Phil. Trans. R. Soc. Lond. A 337 (1991), 429-466
8. Fornberg, B., Whitham, G.B., A numerical and theoretical study of certain nonlinear wave phenomena. Phil. Trans. R. Soc. Lond. A 289 (1978), 373-404
9. Geľfand, I.M., Dorfman, I. Ya. R., Hamiltonian operators and algebraic structures related to them. Func. Anal. Appl. 13 (1979), 248-262
10. Green, A.E., Naghdi, P.M., A derivation of equations for wave propagation in water of variable depth. J. Fluid Mech. 78 (1976), 237-246
11. Holm, D.D., Hamiltonian structure for two dimensional hydrodynamics with nonlinear dispersion. Phys. Fluids 31 (1988), 2371-2373
12. Holm, D.D., Marsden, J.E., Ratiu, T.S., Hamiltonian structure and Lyapunov stability for ideal continuum dynamics., 1985, University of Montreal Press, Montreal
13. Miles, J.W., Salmon, R.M., Weakly dispersive nonlinear gravity waves. J. Fluid Mech. 157 (1985), 519-531
14. Olver, P.J., Hamiltonian perturbation theory and water waves. Contemp. Math., 28, 1984, 231
15. Olver, P.J., Applications of Lie groups to differential equations., 1986, Springer, New York
16. Olver, P.J., Unidirectionalization of Hamiltonian waves. Phys. Lett. A 126 (1988), 501-506
17. Peregrine, Long waves on a beach. J. Fluid Mech. 27 (1967), 815-827
18. Rosenau, P., Hyman, J.M., Compactons: Solitons with finite wavelength. Phys. Rev. Lett. 70 (1992), 564-567
19. B. Wendroff, (1992). Private communication
20. Whitham, G.B., Linear and nonlinear waves., 1974, Wiley, New York
21. Wu, T.Y., Long waves in ocean and coastal waters. J. Eng. Mech. Div., Proc. ASCE 107 (1981), 502-522