Nonlinear parabolic equation and extreme waves on the sea surface

Radiophysics and Quantum Electronics

Volumn 46, Issue 7, 2003, Pages 451-463

  Pelinovsky, E N ^a   Slunyaev, A V ^a   Talipova, T G ^a   Kharif, C ^b  

^a INSTITUTE OF APPLIED PHYSICS   (Russian Federation)

^b AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL NONLINEARITIES; DISPERSION (WAVES); NONLINEAR OPTICS; OCEAN CURRENTS; PARTIAL DIFFERENTIAL EQUATIONS; SURFACE WATERS; WAVE PACKETS;

DINGER EQUATION; FUNDAMENTAL EQUATIONS; NON-STATIONARY WAVES; NONLINEAR PARABOLIC EQUATIONS; PHYSICAL MECHANISM; PHYSICAL NATURE; STRONG DISPERSION; WEAKLY NON-LINEAR;

NONLINEAR EQUATIONS;

EID: 30344487890     PISSN: 00338443     EISSN: 15739120     Source Type: Journal    
DOI: 10.1023/B:RAQE.0000019863.50302.35     Document Type: Article

References (46)

1. L. P. Pitaevskii, Sov. Phys. JETP, 13, 451 (1961).
2. V. I. Talanov, Sov. Phys. JETP Lett., 2, 138 (1965).
3. P. L. Kelley, Phys. Rev. Lett., 15, No. 26, 1005 (1965).
4. L. A. Ostrovskii, Sov. Phys. JETP, 24, 797 (1967).
5. D. J. Benney and A. C. Newell, J. Math. Phys. (Stud. Appl. Math.), 46, 133 (1967).
6. M. I. Rabinovich and D. I. Trubetskov, Oscillations and Waves in Linear and Nonlinear Systems, Kluwer Academic Publ. (1989).
7. M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge Univ. Press (1991).
8. S. N. Vlasov and V. I. Talanov, Self-Focusing of Waves [in Russian], Inst. Appl. Phys. Press, Nizhny Novgorod (1997).
9. V. E. Zakharov, J. Appl. Mech. Tech. Phys., No. 2, 190 (1968).
10. H. Hasimoto and J. Ono, J. Phys. Soc. Japan, 33, 805 (1972).
11. A. Davey, J. Fluid Mech., 53, 769 (1972).
12. T. B. Benjamin and J. E. Feir, J. Fluid Mech., 27, No. 3, 417 (1967).
13. S. E. Sand, N. E. Ottesen Hansen, P. Klinting, O. T. Gudmestad, and M. J. Sterndorff, in: O. Torum and O. T. Gudmestad, eds., Water Wave Kinematics, Kluwer Academic Publ. (1990), p. 535.
14. I. V. Lavrenov, Mathematical Modelling of Wind Roughness in the Spatially Inhomogeneous Ocean [in Russian], Gidrometeoizdat (1998).
15. S. Haver and O. J. Andersen, in: Proc. 10th Conf. ISOPE (42), p. 123.
16. N. Mori, P. C. Liu, and N. Yasuda, Ocean Eng., 29, 1399 (2002).
17. A. K. Magnusson, M. A. Donelan, and W. M. Drennan, Coastal Eng., 36, 147 (1999).
18. K. B. Dysthe and K. Trulsen, Physica Scripta T, 82, 48 (1999).
19. K. L. Henderson, D. H. Peregrine, and J. W. Dold, Wave Motion, 29, 341 (1999).
20. A. R. Osborne, M. Onorato, and M. Serio, Phys. Lett. A, 275, 386 (2000).
21. E. N. Pelinovsky and C. Kharif, Izv. Akad. Inzhen. Nauk RF, 1, 50 (2000).
22. M. G. Brown and A. Jensen, J. Geophys. Res., 106, 16917 (2001).
23. G. Clauss, Appl. Ocean Res., 24, 147 (2002).
24. V. E. Zakharov, J. Appl. Mech. Tech. Phys., No. 2, 190 (1968).
25. M. J. Ablowitz, Kaup D. J., A. C. Newell, and H. Segur, Stud. Appl. Math., 53, 249 (1974).
26. S. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons: the Inverse Scattering Method, Consultants Bureau, New York (1984).
27. A. V. Slunyaev, “Dynamics of large-amplitude internal and surface waves in the ocean,” Ph.D. Thesis [in Russian], Nizhny Novgorod (2002).
28. D. H. Peregrine, J. Austral. Math. Soc., Ser. B, 25, 16 (1983).
29. A. Calini and C. M. Schober, Phys. Lett. A, 298, 335 (2002).
30. M. J. Ablowitz, J. Hammark, D. Henderson, and C. M. Schober, Physica D, 152–153, 416 (2001).
31. I. E. Alber, Proc. Roy. Soc. Lond. A, 363, 525 (1978).
32. M. Onorato, A. R. Osborne, and M. Serio, Phys. Fluids, 14, No. 4, L25 (2002).
33. M. Onorato, A. Osborne, M. Serio, and S. Bertone, Phys. Rev. Lett., 86, No. 25, 5831 (2001).
34. J. C. Bronski and J. N. Kutz, Phys. Lett. A, 254, 325 (1999).
35. M. Desaix, Phys. Rev. Lett., 90, No. 1, article No. 013901 (2003).
36. E. M. Dianov, Z. S. Nikonova, A. M. Prokhorov, and V. M. Serkin, Pis’ma Zh. Tekh. Fiz., 12, No. 12, 756 (1986).
37. C.-M. Chen and P. L. Kelley, J. Opt. Soc. Am. B, 19, No. 9, 1961 (2002).
38. C. Kharif, E. Pelinovsky, T. Talipova, and A. Slunyaev, JETP Lett., 73, 190 (2001).
39. M. J. Ablowitz and H. Segur, J. Fluid Mech., 92, 691 (1979).
40. A. G. Litvak, V. A. Mironov, and É. M. Sher, JETP, 91, 1268 (2000).
41. W. J. D. Bateman, C. Swan, and P. H. Taylor, J. Comput. Phys., 174, 277 (2001).
42. A. Slunyaev, C. Kharif, E. Pelinovsky, and T. Talipova, Physica D, 173, 77 (2002).
43. G. Lawton, New Scientist, 170, 28 (2001).
44. K. Trulsen, in: Proc. Workshop “Rogue Waves 2000” (2000), p. 265.
45. A. G. Litvak and V. I. Talanov, Radiophys. Quantum Electron., 10, No. 4, 296 (1967).
46. D. Clammond and J. Grue, C. R. Mecanique, 330, 575 (2002).