Stability of the NLS equation with viscosity effect

A nonlinear schrdinger (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. copyright © 2011 n. karjanto and k. m. tiong.