Deep-water internal solitary waves near critical density ratio

Physica D: Nonlinear Phenomena

Volumn 225, Issue 2, 2007, Pages 153-168

  Agafontsev, D S ^a   Dias, F ^b   Kuznetsov, E A ^a  

^a LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Hamiltonian description; Lyapunov stability; Sobolev type inequalities; Solitons; Supercritical and subcritical bifurcations

Indexed keywords

BIFURCATION (MATHEMATICS); INTERFACES (MATERIALS); LYAPUNOV METHODS; NONLINEAR EQUATIONS; SOLITONS; SUPERCRITICAL FLUIDS; SYSTEM STABILITY;

HAMILTONIAN DESCRIPTION; LYAPUNOV STABILITY; SOBOLEV TYPE INEQUALITIES; SOLITARY WAVES; SUBCRITICAL BIFURCATIONS;

SHOCK WAVES;

EID: 33845460220     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2006.10.010     Document Type: Article

References (46)

1. Longuet-Higgins M.S. Capillary-gravity waves of solitary type on deep water. J. Fluid Mech. 200 (1989) 451-470
2. Iooss G., and Kirchgässner K. Bifurcation d'ondes solitaires en présence d'une faible tension superficielle. C. R. Acad. Sci. Paris, Série I 311 (1990) 265-268
3. Vanden-Broeck J.-M., and Dias F. Gravity-capillary solitary waves in water of infinite depth and related free-surface flows. J. Fluid Mech. 240 (1992) 549-557
4. Dias F., and Iooss G. Capillary-gravity solitary waves with damped oscillations. Physica D 65 (1993) 399-423
5. Longuet-Higgins M.S. Capillary-gravity waves of solitary type and envelope solitons on deep water. J. Fluid Mech. 252 (1993) 703-711
6. Akylas T.R. Envelope solitons with stationary crests. Phys. Fluids 5 (1993) 789-791
7. Dias F., and Iooss G. Capillary-gravity interfacial waves in deep water. Eur. J. Mech. B Fluids 15 (1996) 367-390
8. Rusas P.-O., and Grue J. Solitary waves and conjugate flows in a three-layer fluid. Eur. J. Mech. B Fluids 21 (2002) 185-206
9. L.D. Landau, E.M. Lifshitz, Statistical Physics, Part 1, Pergamon Press, New York (Original work published 1995, Nauka, Moscow, p. 521) (in Russian)
10. Kuznetsov E.A. Hard soliton excitation: Stability investigation. ZhETF 116 (1999) 299-317
11. Kuznetsov E.A. Hard soliton excitation: Stability investigation. JETP 89 (1999) 163-172
12. Sun S.M. Some analytical properties of capillary-gravity waves in two-fluid flows of infinite depth. Proc. Roy. Soc. Lond. A 453 (1997) 1153-1175
13. Dysthe K.B. Note on a modification to the nonlinear Schrödinger equation for application to deep water waves. Proc. Roy. Soc. Lond. A 369 (1979) 105-114
14. Ablowitz M.J., Hammack J., Henderson D., and Schober C.M. Modulated periodic Stokes waves in deep water. Phys. Rev. Lett. 84 (2000) 887-890 Long-time dynamics of the modulational instability of deep water waves, Physica D 152-153 (2001) 416-433
15. Zakharov V.E., and Kuznetsov E.A. Hamiltonian formalism for nonlinear waves. Usp. Fiz. Nauk 167 (1997) 1137-1168
16. Zakharov V.E., and Kuznetsov E.A. Hamiltonian formalism for nonlinear waves. Phys. Uspekhi 40 (1997) 1087-1116
17. Zakharov V.E., and Kuznetsov E.A. Optical solitons and quasisolitons. Zh. Éksp. Teor. Fiz. 113 (1998) 1892
18. Zakharov V.E., and Kuznetsov E.A. Optical solitons and quasisolitons. JETP 86 (1998) 1035-1046
19. Sinitsyn Yu.A., and Kontorovich V.M. In: Ozmidov R.V. (Ed). Studies of Turbulent Structure of Ocean (First Symposium "Issledovanie melkomaschtabnoi okeanicheskoi turbulentnosti", Kaliningrad, 1974) (1975), Izd. MGI, Sevastopol'
20. Kontorovich V.M. A possible role of internal waves in occurence of small-scale turbulence in stratified ocean. Izv. Vuzov, Radiofizika 19 (1976) 872-879
21. Kuznetsov E.A., and Spector M.D. Existence of hexagon relief on the surface of the liquid dielectrics in an external electric field. Zh. Éksp. Teor. Fiz. 71 (1976) 262
22. Kuznetsov E.A., and Spector M.D. Existence of hexagon relief on the surface of the liquid dielectrics in an external electric field. Sov. Phys. JETP 44 (1976) 136
23. Kuznetsov E.A., Spector M.D., and Zakharov V.E. Surface singularities of ideal fluid. Phys. Lett. 182A (1993) 387-393
24. Dias F., and Bridges T. Geometric aspects of spatially periodic interfacial waves. Stud. Appl. Math. 93 (1994) 93-132
25. Zakharov V.E. Stability of periodic waves of finite amplitude on the surface of a deep fluid. Zh. Prikl. Mekh. Tekh. Fiz. 9 (1968) 86-94
26. Zakharov V.E. Stability of periodic waves of finite amplitude on the surface of a deep fluid. Sov. J. Appl. Mech. Tech. Phys. 9 (1968) 190-194
27. Zakharov V.E., and Filonenko N.N. The energy spectrum for stochastic oscillations of a fluid surface. Dokl. Akad. Nauk SSSR 170 (1966) 1292-1295
28. Zakharov V.E., and Filonenko N.N. The energy spectrum for stochastic oscillations of a fluid surface. Sov. Phys. Dokl. 11 (1967) 881-884
29. Benjamin T.B., and Bridges T.J. Reappraisal of the Kelvin-Helmholtz problem. I. Hamiltonian structure. J. Fluid Mech. 333 (1997) 301-325
30. Craig W., and Groves M.D. Normal forms for wave motion in fluid interfaces. Wave Motion 31 (2000) 21-41
31. Craig W., Guyenne P., and Kalisch H. Hamiltonian long wave expansions for free surfaces and interfaces. Comm. Pure Appl. Math. 58 (2005) 1587-1641
32. Zakharov V.E. Kolmogorov spectra in weak turbulence problems. Basic Plasma Physics. In: Galeev A.A., and Sudan R.N. (Eds). Handbook of Plasma Physics vol. 2 (1984), Elsevier, North-Holland 3-36
33. Newell A.C. Solitons in Mathematics and Physics (1985), SIAM, Philadelphia
34. Dias F., and Kuznetsov E.A. On the nonlinear stability of solitary waves for the fifth-order Korteweg-de Vries equation. Phys. Lett. A 263 (1999) 98-104
35. Laget O., and Dias F. Numerical computation of capillary-gravity interfacial solitary waves. J. Fluid Mech. 349 (1997) 221-251
36. Bridges T.J., Christodoulides P., and Dias F. Spatial bifurcations of interfacial waves when the phase and group velocities are nearly equal. J. Fluid Mech. 285 (1995) 121-158
37. Dyachenko A.I., Korotkevich A.O., and Zakharov V.E. Weak turbulent Kolmogorov spectrum for surface gravity waves. Phys. Rev. Lett. 92 (2004) 134501
38. Zakharov V.E., and L'vov V.S. The statistical description of the nonlinear wave fields. Izv. Vuzov, Radiofizika 18 (1975) 1470-1487
39. Zakharov V.E., and L'vov V.S. The statistical description of the nonlinear wave fields. Radiophys. Quantum Electron. 18 (1975) 1484-1497
40. Iooss G. Existence d'orbites homoclines à un équilibre elliptique, pour un système réversible. C. R. Acad. Sci. Paris 324 (1997) 993-997
41. Kuznetsov E.A., and Turitsyn S.K. Talanov transformations for selffocusing problems and instability of waveguides. Phys. Lett. 112A (1985) 273
42. Kuznetsov E.A., Rubenchik A.M., and Zakharov V.E. Soliton stability in plasmas and fluids. Phys. Rep. 142 (1986) 103
43. Petviashvili V.I. On the equation for unusual soliton. Fiz. Plasmy 2 (1976) 469-472
44. Petviashvili V.I. On the equation for unusual soliton. Sov. J. Plasma Phys. 2 (1976) 247-250 Non-one-dimensional solitons, in: A.V. Gaponov-Grekhov (Ed.), Nonlinear Waves, Nauka, Moscow, 1979, pp. 5-21
45. Vakhitov N.G., and Kolokolov A.A. Stationary solutions of the wave equation in media with saturated nonlinearity. Izv. VUZ Radiofizika 16 (1973) 1020-1028
46. Vakhitov N.G., and Kolokolov A.A. Stationary solutions of the wave equation in media with saturated nonlinearity. Radiophys. Quantum Electron. 16 (1973) 783