New application of the (G'/G)-expansion method to higher-order nonlinear equations

In this paper, we extend the G^'G-expansion method to higher-order nonlinear equations. As a result, a series of new travelling wave solutions of the modified Kawahara equation and the fifth-order KdV equation have been obtained. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. It is shown that the G^'G-expansion method presents a wider applicability for handling nonlinear evolution equations.

[1]  Mingliang Wang,et al.  The (G' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics , 2008 .

[2]  E. Fan,et al.  Extended tanh-function method and its applications to nonlinear equations , 2000 .

[3]  Abdul-Majid Wazwaz,et al.  A study on nonlinear dispersive partial differential equations of compact and noncompact solutions , 2003, Appl. Math. Comput..

[4]  Jiao-Ling Zhang,et al.  A generalized (G′G)-expansion method and its applications , 2008 .

[5]  Sheng Zhang,et al.  The (G′G)-expansion method for nonlinear differential-difference equations , 2009 .

[6]  Mingliang Wang.  SOLITARY WAVE SOLUTIONS FOR VARIANT BOUSSINESQ EQUATIONS , 1995 .

[7]  P. Clarkson,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering: References , 1991 .

[8]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[9]  Ji-Huan He,et al.  Exp-function method for nonlinear wave equations , 2006 .

[10]  İsmail Aslan,et al.  Symbolic Computation and Construction of New Exact Traveling Wave Solutions to Fitzhugh-Nagumo and Klein-Gordon Equations , 2009 .

[11]  Wei Wang,et al.  A generalized (G′G)-expansion method for the mKdV equation with variable coefficients , 2008 .

[12]  Sirendaoreji.  New exact travelling wave solutions for the Kawahara and modified Kawahara equations , 2004 .

[13]  Abdul-Majid Wazwaz,et al.  The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations , 2007, Appl. Math. Comput..

[14]  Ismail Aslan,et al.  Exact and explicit solutions to some nonlinear evolution equations by utilizing the (G'/G)-expansion method , 2009, Appl. Math. Comput..

[15]  Abdul-Majid Wazwaz,et al.  Solitons and periodic solutions for the fifth-order KdV equation , 2006, Appl. Math. Lett..

[16]  Changbum Chun,et al.  Solitons and periodic solutions for the fifth-order KdV equation with the Exp-function method , 2008 .

[17]  Turgut Özis,et al.  Analytic study on two nonlinear evolution equations by using the (G'/G)-expansion method , 2009, Appl. Math. Comput..

[18]  Jinliang Zhang,et al.  Application of the (G'/G)-expansion to travelling wave solutions of the Broer-Kaup and the approximate long water wave equations , 2008, Appl. Math. Comput..

[19]  Turgut Özis,et al.  On the validity and reliability of the (G'/G)-expansion method by using higher-order nonlinear equations , 2009, Appl. Math. Comput..

[20]  Mingliang Wang,et al.  Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics , 1996 .

[21]  İsmail Aslan,et al.  Symbolic Computations and Exact and Explicit Solutions of Some Nonlinear Evolution Equations in Mathematical Physics , 2009 .

[22]  B. Duffy,et al.  An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations , 1996 .

[23]  Q. Al‐Mdallal,et al.  Sine–Cosine method for finding the soliton solutions of the generalized fifth-order nonlinear equation , 2007 .

[24]  Huiqun Zhang,et al.  New application of the (G ′ /G) -expansion method , 2009 .

[25]  Elçin Yusufoglu,et al.  Symbolic computation and new families of exact travelling solutions for the Kawahara and modified Kawahara equations , 2008, Comput. Math. Appl..

[26]  Ahmet Bekir.  Application of the (G′G)-expansion method for nonlinear evolution equations , 2008 .