The Travelling Wave Solutions of the Active-Dissipative Dispersive Media Equation by (G′/G)-Expansion Method

Abstract

AbstractOver 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 μt +μμx + αμxx + βμxxx + γμxxxx = 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 fragmented 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.Keywords(G′/G)-Expansion methodThe active-dissipative dispersive media equationWave solutions