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Modulational instability in asymmetric coupled wave functions

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  • I. Kourakis
  • P. K. Shukla

Abstract

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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Suggested Citation

  • I. Kourakis & P. K. Shukla, 2006. "Modulational instability in asymmetric coupled wave functions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 321-325, March.
    • Handle: RePEc:spr:eurphb:v:50:y:2006:i:1:p:321-325
    DOI: 10.1140/epjb/e2006-00106-1
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    Cited by:

    1. Lazarides, N. & Veldes, Giorgos P. & Javed, Amaria & Kourakis, Ioannis, 2023. "Modulational electrostatic wave–wave interactions in plasma fluids modeled by asymmetric coupled nonlinear Schrödinger (CNLS) equations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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