Abstract
In this paper, we obtain exact solutions of two nonlinear evolution equations, namely the modified Kortweg de Vries equation and the higher-order modified Boussinesq equation with damping term. The method employed to obtain the exact solutions is the (G � /G)-expansion method. Traveling wave solutions of three types are obtained
Highlights
In this paper, we consider two nonlinear evolution equations, namely the modified Kortweg de Vries equation [ ]uuxxt – uxuxt – u ut + uuxxx – uxuxx – u ux = ( )and the higher-order modified Boussinesq equation with damping term [ ]utt + αutxx + βuxxxx + γ u(ux) + u uxx = .It is well known that nonlinear evolution equations, such as ( ) and ( ), are widely used as models to describe physical phenomena in different fields of applied sciences such as plasma waves, solid state physics, plasma physics and fluid mechanics
This paper showed that the (G /G)expansion method is an effective method for finding exact solutions of nonlinear evolution equations
The key ideas of the method are that the traveling wave solutions of a complicated nonlinear evolution equation can be constructed by means of various solutions of a second-order linear ordinary differential equation [ ]
Summary
This paper showed that the (G /G)expansion method is an effective method for finding exact solutions of nonlinear evolution equations. The key ideas of the method are that the traveling wave solutions of a complicated nonlinear evolution equation can be constructed by means of various solutions of a second-order linear ordinary differential equation [ ]. We derive the traveling wave solutions of the two equations by using the (G /G)-expansion method.
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