The travelling wave solutions of the active-dissipative dispersive media equation by (G′/G) -expansion method

Abstract

Over the past decades a number of approximate methods for finding travelling wave solutions to nonlinear evolution equations have been proposed. Among these methods one of the current methods is so called (G′/G) -expansion method. In this paper we will examine the(G′/G) -expansion method for determining the solutions of the active-dissipative dispersive media equation. The active-dissipative dispersive media equation is given by μ<inf>t</inf>+μμ<inf>x</inf>+αμ<inf>xx</inf>+βμ <inf>xxx</inf>+γμ<inf>xxxx</inf> = 0 where for positive constants α and γ in equation are small-amplitude. This equation describe long waves on a viscous fluid flowing down along an inclined plane unstable drift waves in plasma and stress waves in fragmentated porous media. When β = 0 equation is reduced to the Kuramoto-Sivashinsky equation which is the simplest equations that appears in modelling the nonlinear behaviour of disturbances for a sufficiently large class of active dissipative media. It represents the evolution of concentration in chemical reactions hydrodynamic instabilities in laminar flame fronts and at the interface of two viscous fluids. © Springer-Verlag Berlin Heidelberg 2014. © 2014 Elsevier B.V. All rights reserved.