Stability of the NLS equation with viscosity effect
Abstract
A nonlinear Schr\"{o}dinger (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.
Cite
@article{arxiv.1804.06949,
title = {Stability of the NLS equation with viscosity effect},
author = {N. Karjanto and K. M. Tiong},
journal= {arXiv preprint arXiv:1804.06949},
year = {2018}
}
Comments
11 pages, 3 figures