A New (G'/G)-Expansion Method and Its Application to the Burgers Equation

Md. Nur ALAM, M. Ali AKBAR

Abstract


In this article, a new (G'/G)-expansion method is proposed, where G = G(S) satisfies a second order nonlinear ordinary differential equation to seek the travelling wave solutions of nonlinear evolution equations. The Burgers equation is chosen to illustrate the validity and advantages of proposed method. Hyperbolic function, trigonometric function and rational function solutions with arbitrary constants are obtained from which some special solutions, including the known solitary wave solution, are derived by setting the appropriate values of constants. It is shown that the new (G'/G)-expansion method is effective, and gives new, more general, travelling wave solutions than the existing methods, such as the basic (G'/G)-expansion method, the extended (G'/G)-expansion method, the improved (G'/G)-expansion method, the generalized and improved (G'/G)-expansion method etc.

doi:10.14456/WJST.2014.86


Keywords


(G'/G)-expansion method, The Burgers equation, Nonlinear differential equation, Homogeneous balance, Traveling wave solutions, Solitary wave solutions

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References


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