The Travelling Wave Solutions of the Active-dissipative Dispersive Media Equation by (G'/G) -expansion Method

摘要

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_t + μμ_x + αμ_(xx) + βμ_(xxx) + γμ_(xxxx) = 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.