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

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+?µxx+ßµ xxx+?µxxxx = 0, where for positive constants ? and ? 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 ß = 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.