THE ($\frac{G'}{G}$)- EXPANSION METHOD COMBINED WITH THE RICCATI EQUATION FOR FINDING EXACT SOLUTIONS OF NONLINEAR PDES

In this article, we construct exact traveling wave solutions for nonlinear PDEs in mathematical physics via the (1+1)- dimensional combined Korteweg- de Vries and modifled Korteweg- de Vries (KdV- mKdV) equation, the (1+1)- dimensional compouned Korteweg- de Vries Burgers (KdVB) equation,, the (2+1)- dimensional cubic Klien- Gordon (cKG) equation , the Generalized Zakharov- Kuznetsov- Bonjanmin- Bona Mahony (GZK-BBM) equation and the modifled Korteweg- de Vries - Zakharov- Kuznetsov (mKdV-ZK) equation, by using the ( G 0 G ) -expansion method combined with the Riccati equation, where G = G(») satisfles the Riccati equation G 0 (») = A + BG 2 and A, B are arbitrary constants. 0 G )- expansion method, The Riccati equa- tion, Traveling wave solutions, The KdV-mKdV equation, The KdVB equa- tion, The cKG equation , The GZK-BBM equation , The mKdV-ZK equa- tion.

[1]  Zhen Wang,et al.  Many new kinds exact solutions to (2+1)-dimensional Burgers equation and Klein-Gordon equation used a new method with symbolic computation , 2007, Appl. Math. Comput..

[2]  Mingliang Wang,et al.  Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation , 2005 .

[3]  Bin Wu,et al.  Painlevé analysis and special solutions of generalized Broer-Kaup equations , 2002 .

[4]  T. Xia,et al.  New Exact Traveling Wave Solutions for Compound KdV-Burgers Equations in Mathematical Physics ∗† , 2002 .

[5]  Khaled A. Gepreel,et al.  On the solitary wave solutions for nonlinear Hirota–Satsuma coupled KdV of equations , 2004 .

[6]  Sheng Zhang,et al.  A further improved tanh function method exactly solving the -dimensional dispersive long wave equations. , 2008 .

[7]  Ahmet Bekir,et al.  Exact solutions of coupled nonlinear evolution equations , 2008 .

[8]  Deng-Shan Wang,et al.  Further extended sinh-cosh and sin-cos methods and new nontraveling wave solutions of the -dimensional dispersive long wave equations. , 2005 .

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

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

[11]  A. Bekir.  The tanh–coth method combined with the Riccati equation for solving non-linear equation , 2009 .

[12]  E. Zayed,et al.  New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized -expansion method , 2009 .

[13]  Khaled A. Gepreel,et al.  The (G′/G)-expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics , 2009 .

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

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

[16]  Hu Junqi,et al.  An algebraic method exactly solving two high-dimensional nonlinear evolution equations , 2005 .

[17]  Hong Zhao,et al.  Generalized method to construct the solitonic solutions to (3+1)-dimensional nonlinear equation , 2006 .

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

[19]  Tiecheng Xia,et al.  A further improved extended Fan sub-equation method and its application to the (3+1)-dimensional Kadomstev Petviashvili equation , 2006 .

[20]  Nikolai A. Kudryashov,et al.  On types of nonlinear nonintegrable equations with exact solutions , 1991 .

[21]  Sheng Zhang,et al.  APPLICATION OF EXP-FUNCTION METHOD TO HIGH-DIMENSIONAL NONLINEAR EVOLUTION EQUATION , 2008 .

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

[23]  Xiangzheng Li,et al.  Sub-ODE method and solitary wave solutions for higher order nonlinear Schrödinger equation , 2007 .

[24]  Abdul-Majid Wazwaz,et al.  New solutions of distinct physical structures to high-dimensional nonlinear evolution equations , 2008, Appl. Math. Comput..

[25]  Nikolai A. Kudryashov,et al.  Exact solutions of the generalized Kuramoto-Sivashinsky equation , 1990 .

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

[27]  Qi Wang,et al.  Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to (1 + 1)-dimensional dispersive long wave equation , 2005 .

[28]  Sheng Zhang,et al.  Application of Exp-function method to Riccati equation and new exact solutions with three arbitrary functions of Broer–Kaup–Kupershmidt equations , 2008 .

[29]  E. Zayed,et al.  The ( $\frac{G'}{G})$ -expansion method and its applications to some nonlinear evolution equations in the mathematical physics , 2009 .

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

[31]  Zuntao Fu,et al.  JACOBI ELLIPTIC FUNCTION EXPANSION METHOD AND PERIODIC WAVE SOLUTIONS OF NONLINEAR WAVE EQUATIONS , 2001 .

[32]  M. Tabor,et al.  The Painlevé property for partial differential equations , 1983 .

[33]  Xiaoling Zhang,et al.  A new generalized Riccati equation rational expansion method to a class of nonlinear evolution equations with nonlinear terms of any order , 2007, Appl. Math. Comput..

[34]  M. A. Abdou.  The extended tanh method and its applications for solving nonlinear physical models , 2007, Appl. Math. Comput..

[35]  Dazhao Lü,et al.  Jacobi elliptic function solutions for two variant Boussinesq equations , 2005 .

[36]  Gui-qiong Xu.  An elliptic equation method and its applications in nonlinear evolution equations , 2006 .

[37]  Abdul-Majid Wazwaz,et al.  Compact and noncompact physical structures for the ZK-BBM equation , 2005, Appl. Math. Comput..

[38]  Elçin Yusufoğlu.  New solitonary solutions for the MBBM equations using Exp-function method , 2008 .

[39]  Emmanuel Yomba,et al.  The extended Fan's sub-equation method and its application to KdV¿MKdV, BKK and variant Boussinesq equations , 2005 .

[40]  Zhenya Yan,et al.  Abundant families of Jacobi elliptic function solutions of the (2+1)-dimensional integrable Davey–Stewartson-type equation via a new method , 2003 .