Periodic solutions for a complex Hamiltonian system: New standing water-waves

Wave Motion

Volumn 24, Issue 2, 1996, Pages 139-150

  Agnon, Y ^a   Glozman, M ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000471504     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/0165-2125(96)00011-X     Document Type: Article

References (17)

1. J.W. Miles and D.M. Henderson, "Parametrically forced surface waves", Ann. Rev. Fluid Mech. 22, 143-165 (1990).
2. E. Kit, L. Shemer and T. Miloh, "Experimental and theoretical investigation of nonlinear sloshing waves in a rectangular channel", J. Fluid Mech. 181, 265-291 (1987).
3. X.M. Gu and P.R. Sethna, "Resonant surface waves and chaotic phenomena", J. Fluid Mech. 183, 543-565 (1987).
4. J.W. Miles, "Nonlinear Faraday resonance", J. Fluid Mech. 146, 285-302 (1984).
5. J.W.S. Rayleigh, "Deep water waves, progressive or stationary, to the third order of approximation", Proc. Roy. Soc. London Ser. A 97, 345-353 (1915).
6. W.G. Penny and A.T. Price, "Finite periodic stationary gravity waves in a perfect fluid, Part 2", Philos. Trans. Roy. Soc. London Ser. A 244, 254-284 (1952).
7. L.W. Schwartz and A.K. Whitney, "A semi-analytic solution for nonlinear standing waves in deep water", J. Fluid Mech. 107, 147-171 (1981).
8. J.W. Rottman, "Steep standing waves at a fluid interface", J. Fluid Mech. 124, 283-306 (1982).
9. G.N. Mercer and A.J. Robert, "Standing waves in deep water: Their stability and extreme form", Phys. Fluids A 4 (2), 259-269 (1992).
10. M. Glozman, Y. Agnon and M. Stiassnie, "High order formulation of the water-wave problem", Physica D 66, 347-367 (1993).
11. M. Okamura, "Instabilities of weakly nonlinear standing gravity waves", J. Phys. Soc. Japan 53, 3788-3796 (1984).
12. H.C. Yuen and B.M. Lake, "Nonlinear dynamics of deep water gravity waves", Adv. Appl. Mech. 22, 67-229 (1982).
13. V.E. Zakharov, "Stability of periodic waves of finite amplitude on the surface of a deep fluid", Engl. Transl.: J. Appl. Mech. Tech. Phys. 9, 190-194 (1968).
14. H. Goldstein, Classical Mechanics, 2nd Edition, Addison-Wesley, Reading, MA (1980).
15. T.B. Benjamin and J.E. Feir, "The disintegration of wave trains on deep water, Part 1: Theory", J. Fluid Mech. 27, 417-430 (1967).
16. M.S. Longuet-Higgins, "The instabilities of gravity waves of finite amplitude in deep water, Part I: Superharmonics", Proc. Roy. Soc. London. Ser. A 360, 471-488 (1978).
17. M.S. Longuet-Higgins, "The instabilities of gravity waves of finite amplitude in deep water, Part II: Subharmonics", Proc. Roy. Soc. London. Ser. A 360, 489-505 (1978).