Modulational instability in asymmetric coupled wave functions

Abstract

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.

NEXT Sigma-Phi Statistical Physics Conference (2005, Kolymbari, Greece) Proceedings, submitted; v.2 is a shorter version of the text in v.1 (more detailed and somehow more explanatory, yet abbreviated due to submission regulations); some typos corrected as well

References in corpus (3)

• Coupled nonlinear Schroedinger field equations for electromagnetic wave propagation in nonlinear left-handed materials
• Multiple domain formation induced by modulation instability in two-component Bose-Einstein condensates
• Modulational instability criteria for two-component Bose-Einstein condensates

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• Electrostatic wave interaction via asymmetric vector solitons as precursor to rogue wave formation in non-Maxwellian plasmas
• Effects of the third-order dispersion on continuous waves in complex potentials
• Modulational instability and nonlocality management in coupled NLS system