Some new exact solutions of the (2+1)-dimensional variable coefficient Broer-Kaup system using the Exp-function method

By using symbolic computation, we apply the Exp-function method to construct new kinds of solutions of (2+1)-dimensional variable coefficient Broer-Kaup system. We show that the Exp-function method provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

[1]  A. Molabahrami,et al.  Numerical solutions of highly oscillatory integrals , 2008, Appl. Math. Comput..

[2]  Hongyou Wu,et al.  Discretizing constant curvature surfaces via loop group factorizations: The discrete sine- and sinh-Gordon equations☆ , 1995 .

[3]  Mohammad Taghi Darvishi,et al.  Application of He’s Homotopy Perturbation Method to Stiff Systems of Ordinary Differential Equations , 2008 .

[4]  Ji-Huan He,et al.  Addendum:. New Interpretation of Homotopy Perturbation Method , 2006 .

[5]  M. A. Abdou,et al.  NEW PERIODIC SOLUTIONS FOR NONLINEAR EVOLUTION EQUATIONS USING EXP-FUNCTION METHOD , 2007 .

[6]  Emmanuel Yomba The extended F-expansion method and its application for solving the nonlinear wave, CKGZ, GDS, DS and GZ equations , 2005 .

[7]  Mohammad Taghi Darvishi,et al.  New solitary wave and periodic solutions of the foam drainage equation using the Exp-function method , 2009 .

[8]  Jian Zhang,et al.  Applications of the Jacobi elliptic function method to special-type nonlinear equations , 2002 .

[9]  S D Zhu,et al.  Exp-function Method for the Discrete mKdV Lattice , 2007 .

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

[11]  A. A. Soliman,et al.  The numerical simulation for stiff systems of ordinary differential equations , 2007, Comput. Math. Appl..

[12]  B. Kadomtsev,et al.  On the Stability of Solitary Waves in Weakly Dispersing Media , 1970 .

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

[14]  Vladimir E. Zakharov,et al.  Stability of periodic waves of finite amplitude on the surface of a deep fluid , 1968 .

[15]  A. Molabahrami,et al.  A reliable treatment for nonlinear Schrödinger equations , 2007 .

[16]  Ji-Huan He Variational iteration method – a kind of non-linear analytical technique: some examples , 1999 .

[17]  S D Zhu,et al.  Exp-function Method for the Hybrid-Lattice System , 2007 .

[18]  A. Molabahrami,et al.  Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method , 2007 .

[19]  Mohammad Taghi Darvishi,et al.  Numerical and explicit solutions of the fifth-order Korteweg-de Vries equations , 2009 .

[20]  Ji-Huan He Application of homotopy perturbation method to nonlinear wave equations , 2005 .

[21]  Ji-Huan He New interpretation of homotopy perturbation method , 2006 .

[22]  M. A. Abdou,et al.  Application of Exp-function method for nonlinear evolution equations with variable coefficients , 2007 .

[23]  Ji-Huan He Homotopy Perturbation Method for Bifurcation of Nonlinear Problems , 2005 .

[24]  M. Boiti,et al.  Spectral transform for a two spatial dimension extension of the dispersive long wave equation , 1987 .

[25]  M. Ablowitz,et al.  Nonlinear-evolution equations of physical significance , 1973 .

[26]  Li Yi-Shen,et al.  The Exact Solutions of Some (2+1)-Dimensional Integrable Systems , 2002 .

[27]  S. Lou,et al.  Infinitely many Lax pairs and symmetry constraints of the KP equation , 1997 .

[28]  Ji-Huan He SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS , 2006 .

[29]  Weijun Sun,et al.  The repeated homogeneous balance method and its applications to nonlinear partial differential equations , 2006 .

[30]  Sheng Zhang,et al.  Application of Exp-function method to a KdV equation with variable coefficients , 2007 .

[31]  Abdul-Majid Wazwaz,et al.  The tan h method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations , 2005 .