NEW EXACT SOLUTIONS OF SOME NONLINEAR EVOLUTION EQUATIONS BY SUB-ODE METHOD

• Journal title : Honam Mathematical Journal
• Volume 35, Issue 4,  2013, pp.683-699
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2013.35.4.683
Title & Authors
NEW EXACT SOLUTIONS OF SOME NONLINEAR EVOLUTION EQUATIONS BY SUB-ODE METHOD
Lee, Youho; An, Jeong Hyang;

Abstract
In this paper, an improved ($\small{\frac{G^{\prime}}{G}}$)-expansion method is proposed for obtaining travelling wave solutions of nonlinear evolution equations. The proposed technique called ($\small{\frac{F}{G}}$)-expansion method is more powerful than the method ($\small{\frac{G^{\prime}}{G}}$)-expansion method. The efficiency of the method is demonstrated on a variety of nonlinear partial differential equations such as KdV equation, mKd equation and Boussinesq equations. As a result, more travelling wave solutions are obtained including not only all the known solutions but also the computation burden is greatly decreased compared with the existing method. The travelling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. The result reveals that the proposed method is simple and effective, and can be used for many other nonlinear evolutions equations arising in mathematical physics.
Keywords
$\small{\frac{F}{G}}$-expansion method;Travelling wave solutions;Nonlinear partial differential equations;Homogeneous balance;
Language
English
Cited by
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