A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water

Wave Motion

Volumn 24, Issue 3, 1996, Pages 281-289

  Trulsen, Karsten ^a   Dysthe, Kristian B ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES; WATER WAVES;

DEEP WATER; NONLINEAR SCHRODINGER EQUATION; STOKES WAVE;

GRAVITY WAVES;

EID: 0030283527     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-2125(96)00020-0     Document Type: Article

References (16)

1. D.J. Benney and A.C. Newell, "The propagation of nonlinear wave envelopes", J. Math. Phys. 46, 133-139 (1967).
2. D.J. Benney and G.J. Roskes, "Wave instabilities", Studies Appl. Math. 48, 377-385 (1969).
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, 455-472 (1986).
4. D.R. Crawford, P.G. Saffman and H.C. Yuen, "Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves", Wave Motion 2, 1-16 (1980).
5. A. Davey, "The propagation of a weak nonlinear wave", J. Fluid Mech. 53, 769-781 (1972).
6. K.B. Dysthe, "Note on a modification to the nonlinear Schrödinger equation for application to deep water waves", Proc. Roy. Soc. Lond. Ser. A 369, 105-114 (1979).
7. H. Hasimoto and H. Ono, "Nonlinear modulation of gravity waves", J. Phys. Soc. Japan 33, 805-811 (1972).
8. E. Lo and C.C. Mei, "A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation", J. Fluid Mech. 150, 395-416 (1985).
9. E.Y. Lo and C.C. Mei, "Slow evolution of nonlinear deep water waves in two horizontal directions: A numerical study", Wave Motion 9, 245-259 (1987).
10. D.U. Martin and H.C. Yuen, "Quasi-recurring energy leakage in the two-space-dimensional nonlinear Schrödinger equation", Phys. Fluids 23, 881-883 (1980).
11. J.W. McLean, "Instabilities of finite-amplitude water waves", J. Fluid Mech. 114, 315-330 (1982).
12. J.W. McLean, "Instabilities of finite-amplitude gravity waves on water of finite depth", J. Fluid Mech. 114, 331-341 (1982).
13. J.W. McLean, Y.C. Ma, D.U. Martin, P.G. Saffman and H.C. Yuen, "Three-dimensional instability of finite-amplitude water waves", Phys. Rev. Lett. 46, 817-820 (1981).
14. O.M. Phillips, "On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions", J. Fluid Mech. 9, 193-217 (1960).
15. M. Stiassnie and L. Shemer, "On modifications of the Zakharov equation for surface gravity waves", J. Fluid Mech. 143, 47-67 (1984).
16. V.E. Zakharov, "Stability of periodic waves of finite amplitude on the surface of a deep fluid", J. Appl. Mech. Tech. Phys. 9, 190-194 (1968).