Higher-Order Approximations for Symmetrical Regular Long Wave Equation

Abstract

In this work, we extend the application of “the modified reductive perturbation method” to the symmetrical regular long wave equation and try to obtain the contribution of higher-order terms in the perturbation expansion. It is shown that the lowest-order term in the expansion is governed by the nonlinear Schrödinger equation while the second- and third-order terms are governed by the linear Schrödinger equation. By employing the hyperbolic tangent method, progressive wave type solutions are obtained for the first-, second- and third-order terms in the perturbation expansion. - PACS numbers: 02.30.Jr, 42.25.Bs, 42.81.Dp, 43.35.Kp