Abstract
In this Letter, the G’/G-expansion method [M.L. Wang, X.Z. Li, J.L. Zhang, Phys. Lett. A 372 (2008) 417] is improved and an extended G’/G -expansion method is proposed to seek the travelling wave solutions of nonlinear evolution equations. We choose the mKdV equation to illustrate the validity and advantages of the proposed method. Many new and more general solutions are obtained. Our solutions naturally include those in open literature.
Highlights
During the past four decades or so searching for explicit solutions of nonlinear evolution equations by using various different methods is the main goal for many researchers, and many powerful methods to construct exact solutions of nonlinear evolution equations have been established and developed such as the inverse scattering transform [1], the Backlund/ Darboux transform [2], the tanh-function expansion and its various extension [3], the exp-function expansion method [4,5,6,7,8,9] and so on, but there is no unified method that can be used to deal with all types of nonlinear evolution equations
Wang et al [10] introduced an expansion technique called the G’/G -expansion method and they demonstrated that it was a powerful technique for seeking analytic solutions of nonlinear partial differential equations
By taking u(x,t) = U (ξ ),ξ = x −Vt, we look for traveling wave solutions of
Summary
During the past four decades or so searching for explicit solutions of nonlinear evolution equations by using various different methods is the main goal for many researchers, and many powerful methods to construct exact solutions of nonlinear evolution equations have been established and developed such as the inverse scattering transform [1], the Backlund/ Darboux transform [2], the tanh-function expansion and its various extension [3], the exp-function expansion method [4,5,6,7,8,9] and so on, but there is no unified method that can be used to deal with all types of nonlinear evolution equations. Bekir [11] and Zedan[12] applied this method to obtain traveling wave solutions of various equations. We shall improve the G’/G -expansion method [10] and propose an extended G’/G -expansion method to seek the travelling wave solutions of nonlinear evolution equations. Equating the coefficients of each power of G’/G to zero, obtain a system of algebraic equations for ai , λ, μ and V To determine these constants, solve the system with the aid of a computer algebra system.
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