Stability of the NLS Equation with Viscosity Effect

[摘要] 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 solutionof the NLS equation exhibits modulational instability phenomenon. In this paper, themodulational instability of the plane-wave solution of the NLS equation modified withviscosity is investigated. The corresponding modulational dispersion relation is expressedas a quadratic equation with complex-valued coefficients. By restricting the modulationalwavenumber 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.

[学科分类] 应用数学