Modulational instability in asymmetric coupled wave functions
Fakultät für Physik und Astronomie, Ruhr-Universität Bochum, 44780 Bochum, Germany
Revised: 21 November 2005
Published online: 12 April 2006
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schrödinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and the group velocity dispersion 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.
PACS: 05.45.Yv – Solitons / 42.65.Sf – Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics / 42.65.Jx – Beam trapping, self-focusing and defocusing; self-phase modulation / 52.35.Mw – Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006