Document Type : Research Paper

Authors

DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, UNIVERSITY OF GUILAN, P.C. 41938, RASHT, IRAN

Abstract

In this paper, the Exp-function method, with the aid of a symbolic computation system such as Maple, is applied to the (2+1) -dimensional Calogero Bogoyavlanskii Schiff equation. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. The method is straightforward and concise, and its applications are promising. It is shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving Calogero Bogoyavlanskii Schiff equation.

Keywords

[1] Wazwaz A. M., The Tanh method: Exact solutions of the Sine–Gordon and Sinh–Gordon equations, Appl. Math. Comput. 167, 1196–1210, 2005.
[2] Iet M., Hereman W., The tanh method: I. Exact solutions of nonlinear evolution and wave equations, Phys. Scr., 54:563–8, 1996.    
 [3] Wazwaz A. M., The tanh and the sine–cosine methods for a reliable treatment of the modified equal width equation and its variants, Commun. Nonlinear Sci. Numer. Simul., 11, 148–160, 2006. 
[4] Biazar J., Ghazvini H., Exact solutions for non-linear Schrödinger equations by He’s homotopy perturbation method Physics Letters A 366, 79-84, 2007.
[5] He J. H., Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals 26, 695–700, 2005.
[6] He J. H., Variational iteration method—a kind of non-linear analytical technique: some examples, Int. J. Nonlinear Mech. 34, 699–708, 1999.
[7] He J. H., Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput. 114, 115–123, 2000.
[8] Biazar J., Babolian E., Nouri A., and Islam R., An alternate algorithm for computing Adomian Decomposition method in special cases, Applied Mathematics and Computation 38 (2-3), 523- 529, 2003.
[9] He J. H., Wu, X.H., Exp-function method for nonlinear wave equations, Chaos Solitons Fractals 30, 700–708, 2006.
[10] Zhang S., Application of Exp-function method to a KdV equation with variable coefficients, Phys. Lett. A, 365, 448–453, 2007.
[11] Ebaid Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method, Phys.Lett. A 365, 213–219, 2007.
[12] Zhu S. D., Exp-function method for the hybrid-lattice system, Int. J. Nonlinear Sci. Numer. Simul. 8,461–464, 2007.
[13] Zhu S. D., Exp-function method for the discrete mKdV lattice, Int. J. Nonlinear Sci. Numer. Simul., 8 ,465–469, 2007.
[13] Biazar J., Ayati Z., Application of Exp-function method to Equal-width wave equation, Physica Scripta, 78 045005, 2008.
[14] Wazwaz A. M., New solutions of distinct physical structures to high-dimensional nonlinear evolution equations, Appl. Math. Comput. 196, 363-370, 2008.
[15] Wazwaz A. M., Multiple-soliton solutions for the Calogero – Bogoyavlenskii-schiff, Jimbo- Miuva and YTSF equations, Appl. Math. Comput, 203, 592-597, 2008.