Copyright © 2011 N. Karjanto and K. M. Tiong. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.