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

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 242)

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 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 method The active-dissipative dispersive media equation Wave solutions 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Science and Letters FacultyYaşar UniversityBornova-İzmirTurkey
  2. 2.Department of Mathematics, Science FacultyEge UniversityBornova-İzmirTurkey

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