Modulation of generalized symmetric regularized long-wave equation: generalized nonlinear Schrödinger equation

Abstract

In this work, the application of "the modified reductive perturbation method" is extended to the generalized symmetric regularized long-wave equation for strongly dispersive case and the contribution of higher order terms in the perturbation expansion is obtained. It is shown that the first order term in the perturbation expansion is governed by the generalized nonlinear Schrödinger quation whereas the second order term is governed by the generalized linear Schrödinger equation with a nonhomogeneous term. A travelling wave type of solution to these evolution equations is also given.