How far one can go with the Exp-function method?

A criterion determining if an exact solution of a differential equation can be expressed in a form comprising a finite number of exponential functions is constructed in this paper. This criterion is based on the concept of ranks of Hankel matrixes constructed from sequences of coefficients produced by symbolic multiplicative operator techniques. The employment of this criterion also gives an answer on the structure of the solution. Several examples are used to illustrate this concept.

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

[2]  Z. Navickas.  Operator Method of Solving Nonlinear Differential Equations , 2002 .

[3]  Feyed Ben Zitoun,et al.  A method for solving nonlinear differential equations , 2010, Kybernetes.

[4]  A. Bekir,et al.  Exact solutions for nonlinear evolution equations using Exp-function method , 2008 .

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

[6]  Abdelhalim Ebaid,et al.  Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method , 2007 .

[7]  Fei Xu,et al.  Application of Exp-function method to Symmetric Regularized Long Wave (SRLW) equation , 2008 .

[8]  Zenonas Navickas,et al.  EXPRESSIONS OF SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS BY STANDARD FUNCTIONS , 2006 .

[9]  Sheng Zhang.  Exp-function method exactly solving a KdV equation with forcing term , 2008, Appl. Math. Comput..

[10]  A. A. Soliman,et al.  Exact solutions of KdV-Burgers' equation by Exp-function method , 2009 .

[11]  Sheng Zhang,et al.  Exp-function method for solving Maccari's system , 2007 .

[12]  A. A. Soliman,et al.  New application of Exp-function method for improved Boussinesq equation , 2007 .

[13]  Zenonas Navickas,et al.  Computer Realization of the Operator Method for Solving of Differential Equations , 2004, NAA.

[14]  Abdul-Majid Wazwaz,et al.  The extended tanh method for new compact and noncompact solutions for the KP–BBM and the ZK–BBM equations , 2008 .

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

[16]  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 .

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

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

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

[20]  Shun-dong Zhu,et al.  Discrete (2 + 1)-dimensional Toda lattice equation via Exp-function method , 2008 .

[21]  W. Hereman,et al.  The tanh method: I. Exact solutions of nonlinear evolution and wave equations , 1996 .

[22]  E. Yusufoglu,et al.  New solitonary solutions for modified forms of DP and CH equations using Exp-function method , 2009 .

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