Dynamics of counterpropagating waves in parametrically driven systems: Dispersion vs. advection

Physica D: Nonlinear Phenomena

Volumn 174, Issue 1-4, 2003, Pages 198-217

  Martel, Carlos ^a   Vega, José M ^a   Knobloch, Edgar ^b  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Counterpropagating waves; Faraday waves; Parametric resonance; Weak dispersion

Indexed keywords

CHAOS THEORY; DISPERSIONS; DYNAMICS; FARADAY EFFECT;

ADVECTION;

WAVE PROPAGATION;

EID: 0037212147     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(02)00691-7     Document Type: Conference Paper

References (24)

1. Bondila M., Barashenkov I.V., Bogdan M.M., Topography of attractors of the parametrically driven nonlinear Schrödinger equation. Physica D. 87:1995;314-320.
2. Barashenkov I.V., Zemlyanaya E.V., Stable complexes of parametrically driven, damped nonlinear Schrödinger solitons. Phys. Rev. Lett. 83:1999;2568-2571.
3. Wang X., Parametrically excited nonlinear waves and their localizations. Physica D. 154:2001;337-359.
4. Daniels P.G., Finite amplitude two-dimensional convection in a finite rotating system. Proc. R. Soc. Lond. A. 363:1978;195-215.
5. Ezerskii A.B., Rabinovich M.I., Reutov V.P., Starobinets I.M., Spatiotemporal chaos in the parametric excitation of a capillary ripple. Sov. Phys. JETP. 64:1986;1228-1236.
6. Martel C., Vega J.M., Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability. Nonlinearity. 11:1998;105-142.
7. Ezerskii A.B., Shekhov V.G., Spatiotemporal modulation of surface waves generated by a uniform field. Sov. Phys. Technol. Phys. 34:1989;386-391.
8. Vega J.M., Knobloch E., Martel C., Nearly inviscid Faraday waves in annular containers of moderately large aspect ratio. Physica D. 154:2001;313-336.
9. G.P. Agrawal, Nonlinear Fiber Optics, Optics and Photonics, Academic Press, New York, 1995.
10. Aceves A.B., Optical gap solitons: past, present and future; theory and experiments. Chaos. 10:2000;584-589.
11. O. Thual, S. Douady, S. Fauve, Parametric instabilities, in: E. Tirapegui, D. Villaroel (Eds.), Instabilities and Nonequilibrium Structures II, Kluwer Academic Publishers, Dordrecht, 1989, pp. 227-237.
12. Martel C., Knobloch E., Vega J.M., Dynamics of counterpropagating waves in parametrically forced systems. Physica D. 137:2000;94-123.
13. Martel C., Vega J.M., Finite size effects near the onset of the oscillatory instability. Nonlinearity. 9:1996;1129-1171.
14. Martel C., Vega J.M., Global stability properties of a hyperbolic system arising in pattern formation. Nonlinear Anal. TMA. 29:1997;439-460.
15. A.C. Newell, Solitons in Mathematics and Physics, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1985.
16. P.G. Drazin, R.S. Johnson, Solitons: An Introduction, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1993.
17. P.D. Lax, C.D. Levermore, S. Venakides, The generation and propagation of oscillations in dispersive IVPs and their limiting behavior, in: T. Fokas, V.E. Zakharov (Eds.), Important Developments in Soliton Theory 1980-1990, Springer, Berlin, 1993, pp. 205-241.
18. Spina A., Toomre J., Knobloch E., Confined states in large aspect ratio thermosolutal convection. Phys. Rev. E. 57:1998;524-545.
19. Barashenkov I.V., Smirnov Y.S., Existence and stability chart for the ac-driven, damped nonlinear Schrödinger solitons. Phys. Rev. E. 54:1996;5707-5725.
20. Barashenkov I.V., Smirnov Y.S., Alexeeva N.V., Bifurcation to multisoliton complexes in the ac-driven, damped nonlinear Schrödinger equation. Phys. Rev. E. 57:1998;2350-5764.
21. Barashenkov I.V., Zemlyanaya E.V., Existence threshold for the ac-driven damped nonlinear Schrödinger solitons. Physica D. 132:1999;363-372.
22. Riecke H., Kramer L., The stability of standing waves with small group velocity. Physica D. 137:2000;124-142.
23. H.Riecke, Crawford J.D., E.Knobloch, Time-modulated oscillatory convection. Phys. Rev. Lett. 61:1988;1942-1945.
24. Higuera M., Porter J., Knobloch E., Heteroclinic dynamics in the nonlocal parametrically driven nonlinear Schrödinger equation. Physica D. 162:2002;155-187.