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Stability of the NLS Equation with Viscosity Effect

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  • N. Karjanto
  • K. M. Tiong

Abstract

A nonlinear Schrödinger (NLS) equation with an effect of viscosity is derived from a Korteweg-de Vries (KdV) equation modified with viscosity using the method of multiple time scale. It is well known that the plane-wave solution of the NLS equation exhibits modulational instability phenomenon. In this paper, the modulational instability of the plane-wave solution of the NLS equation modified with viscosity is investigated. The corresponding modulational dispersion relation is expressed as a quadratic equation with complex-valued coefficients. By restricting the modulational wavenumber into the case of narrow-banded spectra, it is observed that a type of dissipation, in this case the effect of viscosity, stabilizes the modulational instability, as confirmed by earlier findings.

Suggested Citation

  • N. Karjanto & K. M. Tiong, 2011. "Stability of the NLS Equation with Viscosity Effect," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-11, May.
    • Handle: RePEc:hin:jnljam:863161
    DOI: 10.1155/2011/863161
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