Finding general and explicit solutions of high nonlinear equations by the Exp-Function method

In this paper, Davey-Stewartson equation and coupled Klein-Gordon-Schrodinger (KGS) equations and homogeneous nonlinear convection-diffusion problem are solved using the Exp-function method. The capabilities and wide-range applications of the Exp-function method are illustrated. This method can be used as an alternative to obtain analytical and approximate solutions of different types of differential equations in engineering mathematics.

[1]  Ji-Huan He,et al.  Comparison of homotopy perturbation method and homotopy analysis method , 2004, Appl. Math. Comput..

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

[3]  Ji-Huan He,et al.  Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method , 2007, Comput. Math. Appl..

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

[5]  S. Momani An algorithm for solving the fractional convection–diffusion equation with nonlinear source term , 2007 .

[6]  Ji-Huan He,et al.  Homotopy perturbation method: a new nonlinear analytical technique , 2003, Appl. Math. Comput..

[7]  Mingliang Wang,et al.  The periodic wave solutions for the Klein–Gordon–Schrödinger equations , 2003 .

[8]  J. Miller Numerical Analysis , 1966, Nature.

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

[10]  Xu-Hong Wu,et al.  EXP-function method and its application to nonlinear equations , 2008 .

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

[12]  Ji-Huan He,et al.  Asymptotology by homotopy perturbation method , 2004, Appl. Math. Comput..

[13]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[14]  Ji-Huan He,et al.  Variational iteration method for autonomous ordinary differential systems , 2000, Appl. Math. Comput..

[15]  Ji-Huan He A coupling method of a homotopy technique and a perturbation technique for non-linear problems , 2000 .

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

[17]  Davood Domiri Ganji,et al.  Approximate general and explicit solutions of nonlinear BBMB equations by Exp-Function method , 2009 .

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

[19]  Ji-Huan He,et al.  Generalized solitary solution and compacton-like solution of the Jaulent–Miodek equations using the Exp-function method , 2008 .

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