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

DOI10.1016/S0167-2789(02)00691-7zbMath1076.35543MaRDI QIDQ1851382

Carlos Martel, José M. Vega, Edgar Knoblauch

Publication date: 16 December 2002

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

Faraday wavesParametric resonanceCounterpropagating wavesWeak dispersion

Mathematics Subject Classification ID

Nonlinear effects in hydrodynamic stability (76E30) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items

On the exchange of energy in coupled Klein --- Gordon equations, Interaction of free Rossby waves with semi-transparent equatorial waveguide. I: Wave triads, On the construction of the exact analytic or parametric closed-form solutions of standing waves concerning the cubic nonlinear Schrödinger equation, Dispersive destabilization of nonlinear light propagation in fiber Bragg gratings, Interaction of two quasi-monochromatic waves in shallow water, Modulational instability of two pairs of counter-propagating waves and energy exchange in a two-component system, Dispersive destabilization of nonlinear light propagation in fiber Bragg gratings: A numerical verification

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Topography of attractors of the parametrically driven nonlinear Schrödinger equation
• Existence threshold for the ac-driven damped nonlinear Schrödinger solitons
• Dynamics of counterpropagating waves in parametrically forced systems
• The stability of standing waves with small group velocity
• Optical gap solitons: Past, present, and future; theory and experiments
• Finite amplitude two-dimensional convection in a finite rotating system
• Global stability properties of a hyperbolic system arising in pattern formation
• Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability
• Finite size effects near the onset of the oscillatory instability
• Nearly inviscid Faraday waves in annular containers of moderately large aspect ratio
• Parametrically excited nonlinear waves and their localizations
• Heteroclinic dynamics in the nonlocal parametrically driven nonlinear Schrödinger equation