Solitary wave decay in non-linear Faraday resonance

European Journal of Mechanics, B/Fluids

Volumn 18, Issue 1, 1999, Pages 93-102

  Bakholdin, I ^a   Il'ichev, A ^b,c  

^a KELDYSH INSTITUTE OF APPLIED MATHEMATICS   (Russian Federation)

^b UNIVERSITY OF STUTTGART   (Germany)

^c STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

Faraday resonance; Solitary waves; Transition to instability

Indexed keywords

EQUATIONS OF MOTION; NATURAL FREQUENCIES; OSCILLATIONS; PARTIAL DIFFERENTIAL EQUATIONS; RESONANCE;

FARADAY RESONANCE; MILES EQUATION; MODULATED CROSS-WAVES;

WAVEFORM ANALYSIS;

EID: 0032652099     PISSN: 09977546     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0997-7546(99)80007-7     Document Type: Article

References (21)

1. ABLOVITZ M. J., HERBST B. M., 1990, On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation, SIAM J. Appl. Math., 50, 339-351.
2. ABLOVITZ M. J., HERBST B. M., SCHOBER C. M., 1996, Computational chaos in the nonlinear Schrödinger equation without homoclinic crossings, Physica A, 228, 212-235.
3. BAKHOLDIN I. B., 1994, Wave jumps in media described by a modified Schrödinger equation, Fluid Dynamics, 29, 528-538.
4. BAKHOLDIN I., IL'ICHEV A., 1996, Radiation and modulational instability described by the fifth-order Korteweg-de Vries equation, Contemporary Mathematics, 200, 1-15.
5. BARASHENKOV I. V., BOGDAN M. M., KOROBOV V. I., 1991, Stability diagram of the phase-locked solitons in the parametrically driven, damped nonlinear Schrödinger equation, Europhys. Lett., 15, 113-118.
6. BENILOV E. S., GRIMSHAW R., KUZNETSOVA E. P., 1993, The generation of radiating waves in a singularly-perturbed Kortewed-de Vries equation, Physica D, 69, 270-278.
7. CHEN X.-N., WEI R., 1994, Dynamic behaviour of a non-propagating soliton under a periodically modulated oscillation, J. Fluid Mech., 259, 291-303.
8. CHEN X.-N., WEI R., 1996, Chaotic motion of a non-propagating soliton through a period-doubling route, in Nonlinear acoustics in perspective, ed. R. J. Wei, 353-361, Nanjing University Press.
9. CILIBERTO S., Gollub J. P., 1985, Chaotic mode competition in parametrically forced surface waves, J. Fluid, Mech., 158, 381-398.
10. FRIEDEL H., LAEDKE E. W., SPATSCHEK K. H., 1995, Bifurcations and nonlinear dynmics of surface waves in Faraday resonance, J. Fluid Mech., 284, 341-358.
11. IL'ICHEV A., 1998, Faraday resonance: asymptotic theory of surface waves, to appear in Phvsica D.
12. KAMBE T., UMEKI M., 1990, Nonlinear dynamics of two-mode interactions in parametric excitation of surface waves, J. Fluid Mech., 212, 373-393.
13. LAEDKE E. W., SPATSCHEK K. H., 1991, On localized solutions in nonlinear Faraday resonance, J. Fluid Mech., 223, 589-601.
14. LAZZARA A., PUTTERMAN S., 1984, Theory of non-propagating surface-wave solitons, J. Fluid Mech., 148, 443-449.
15. McLAUGHLIN D. W., SCHOBER C. M., 1992, Chaotic and homoclinic behaviour for numerical discretizations of the nonlinear Schrödinger equation, Physica D, 57, 447-465.
16. MILES J., 1984, Parametrically exited solitary waves, J. Fluid Mech., 148, 451-460.
17. MILES J., HENDERSON D., 1990, Parametrically forced surface waves, Ann. Rev. Fluid Mech., 22, 143-165.
18. SAMARSKII A. A., 1977, Theory of difference schemes, Nauka, Moskow, USSR.
19. UMEKI M., 1991a, Parametric dissipative nonlinear Schrödinger equation, J. Phys. Soc. Jpn., 60, 146-167.
20. UMEKI M., 1991b, Faraday resonance in rectangular geometry, J. Fluid Mech., 227, 161-192.
21. WU J., KEOLIAN R., RUDNIK I., 1984, Observation of non-propagating hydrodynamic soliton, Phys. Rev. Lett., 52, 1421-1424.