具有粘性效应的NLS方程的稳定性
Stability of the NLS equation with viscosity effect
摘要：
利用多时间尺度方法，从含粘性修正的KdV方程出发，导出了含粘性效应的非线性薛定谔方程.众所周知，NLS方程的平面波解存在调制不稳定现象。本文研究了带粘性修正的NLS方程平面波解的调制不稳定性。相应的调制色散关系表示为一个二次方程与复值系数。通过限制的调制波数到窄带光谱的情况下，它是观察到的一种类型的耗散，在这种情况下，粘度的影响，稳定的调制不稳定性，证实了早期的研究结果。
英文摘要：
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-scales. 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.
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