Classifying Traveling Wave Solutions to the Zhiber-Shabat Equation

Chunyan Wang, Xinghua Du

Department of Mathematics, Northeast Petroleum University, Daqing, China.
Department of Mathematics, Northeast Petroleum University, Daqing, China..

DOI: 10.4236/jamp.2013.12001                

Abstract

By the complete discrimination system for polynomials, we classify exact traveling wave solutions to the Zhiber-Shabat equation, and compute some new traveling wave solutions.

Keywords

Traveling Wave Solution; Complete Discrimination System for Polynomials; The Zhiber-Shabat Equation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	W. X. Ma, “Integrability,” In: A. Scott, Ed., Encyclopedia of Nonlinear Science, Taylor-Francis, London, 2005, pp. 250-253.
[2]	W. X. Ma and J. H. Lee, “A Transformed Rational Func tion Method and Exact Solutions to the 3+1 Dimensional Jimbo-Miwa Equation,” Chaos, Solitons-Fractals, Vol. 42, No. 3, 2009, pp. 1356-1363. doi:10.1016/j.chaos.2009.03.043
[3]	W. X. Ma and Z. N. Zhu, “Solving the (3+1)-Dimen sional Generalized KP and BKP Equations by the Multi ple Exp-Function Algorithm,” Applied Mathematics and Computation, Vol. 218, No. 24, 2012, pp. 11871-11879. doi:10.1016/j.amc.2012.05.049
[4]	O. Cornejo-Pérez, J. Negro, L. M. Nieto and H. C. Rosu, “Traveling-Wave Solutions for Korteweg-de Vries Bur gers Equations through Factorizations,” Foundations of Physics, Vol. 36, No. 10, 2006, pp. 1587-1599. doi:10.1007/s10701-006-9069-5
[5]	W. X. Ma, “Complexiton Solutions to the Korteweg-de Vries Equation,” Physics Letters A, Vol. 301, No. 1-2, 2002, pp. 35-44. doi:10.1016/S0375-9601(02)00971-4
[6]	W. X. Ma and K. Maruno, “Complexiton Solutions of the Toda Lattice Equation,” Physica A: Statistical Mechanics and Its Applications, Vol. 343, 2004, pp. 219-237.
[7]	C. S. Liu, “Applications of Complete Discrimination System for Polynomial for Classifications of Traveling Wave Solutions to Nonlinear Differential Equations,” Computer Physics Communications, Vol. 181, No. 2, 2010, pp. 317-324. doi:10.1016/j.cpc.2009.10.006
[8]	C. Y. Wang, J. Guan and B. Y. Wang, “The Classification of Single Travelling Wave Solutions to the Camassa Holm-Degasperis-Procesi Equation for Some Values of the Convective Parameter,” Pramana, Vol. 77, No. 4, 2011, pp. 759-764. doi:10.1007/s12043-011-0098-z
[9]	A. M. Wazwaz, “Traveling Wave Solutions to the Zhiber Shabat Equation and Other Related Equations,” Commu nications in Nonlinear Science and Numerical Simulation, Vol. 13, No. 3, 2008, pp. 584-592. doi:10.1016/j.cnsns.2006.06.014
[10]	A. G. Davodi and D. D. Ganji, “Travelling Wave Solu tions to the Zhiber-Shabat and Related Equation Using Rational Hyperbolic Methods,” Advances in Applied Ma thematics and Mechanics, Vol. 2, No. 1, 2010, pp. 118 130.