Modulational instability in asymmetric coupled wave functions

Details Modulational instability in asymmetric coupled wave functions Modulational instability in asymmetric coupled wave functions

2005-10-13

arxiv.org/abs/nlin/0510029v2

Nonlinear Sciences

Pattern Formation and Solitons

NEXT Sigma-Phi Statistical Physics Conference (2005, Kolymbari, Greece) Proceedings, submitted; v.2 is a shorter version of th

Scientific paper

10.1140/epjb/e2006-00106-1

The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and the GVD terms) and the nonlinearity and coupling coefficients, on which no assumption is made. A generalized dispersion relation is obtained, relating the frequency and wave-number of a small perturbation around a coupled monochromatic (Stokes') wave solution. Explicitly stability criteria are obtained. The analysis reveals a number of possibilities. Two (individually) stable systems may be destabilized due to coupling. Unstable systems may, when coupled, present an enhanced instability growth rate, for an extended wave number range of values. Distinct unstable wavenumber windows may arise simultaneously.

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