Abstract
A modification of the generalized projective Riccati equation method is proposed to treat some nonlinear evolution equations and obtain their exact solutions. Some known methods are obtained as special cases of the proposed method. In addition, the method is implemented to find new exact solutions for the well-known Dreinfelds-Sokolov-Wilson system of nonlinear partial differential equations.
Highlights
The investigation of exact travelling wave solutions to nonlinear evolution equations (NLEE's) plays an important role in the study of nonlinear phenomena in many fields such as physics, biology, chemistry and mechanics, etc
This paper is organized as follows: in section 2, we describe the modified generalized projective Riccati equation method
The main steps of the sech tanh method are as follow: We assume the solution of the ordinary differential equation (ODE) (3) is in the form: n u( ) a0 i 1( ) ai ( ) bi ( ), i1 with
Summary
The investigation of exact travelling wave solutions to nonlinear evolution equations (NLEE's) plays an important role in the study of nonlinear phenomena in many fields such as physics, biology, chemistry and mechanics, etc. Due to the increasing interest in obtaining exact solutions of nonlinear partial differential equations (NLPDE's), many powerful methods are available for treating and obtaining solitary wave solutions. They have been developed since the establishment of the inverse scattering technique [1], Backland and Darboux transform [2,3,4], Hirota method [5], Jacobi elliptic function method [6], Hyperbolic functions expansion method [7], tanh method [8], cosine-function method [9], the auxiliary equation method [10], Mapping method [11], and so on.
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