Application of Classification of Traveling Wave Solutions to the Zakhrov-Kuznetsov-Benjamin-Bona-Mahony Equation

Li Yang

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

DOI: 10.4236/am.2014.510135                

Abstract

In order to get the traveling wave solutions of the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation, it is reduced to an ordinary differential equation (ODE) under the travelling wave transformation first. Then complete discrimination system for polynomial is applied to the ZK-BBM equation. The traveling wave solutions of the equation can be obtained.

Keywords

The Nonlinear Partial Differential Equation, The Zakharov-Kuznetsov-Benjamin-Bona-Mahony Equation, Traveling Wave Transform, Complete Discrimination System for Polynomial, The Traveling Wave Solution

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Liu, C.S. (2006) Direct Integral Method, Complete Discrimination System for Polynomial and Applications to Classifications of All Single Traveling Wave Solutions to Nonlinear Differential Equations: A Survey. arXiv preprint nlin/0609058v1.
[2]	Liu, C.S. (2007) Classification of All Single Travelling Wave Solutions to Calogero-Degasperis-Focas Equation. Communications in Theoretical Physics, 48, 601-604. http://dx.doi.org/10.1088/0253-6102/48/4/004
[3]	Liu, C.S. (2010) Applications of Complete Discrimination System for Polynomial for Classifications of Traveling Wave Solutions to Nonlinear Differential Equations. Computer Physics Communications, 181, 317-324. http://dx.doi.org/10.1016/j.cpc.2009.10.006
[4]	Liu, C.S. (2008) Solution of ODE and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations. Communications in Theoretical Physics, 49, 291-296. http://dx.doi.org/10.1088/0253-6102/49/2/07
[5]	Peregrine, D.H. (1967) Long Waves on a Beach. Journal of Fluid Mechanics, 27, 815-827. http://dx.doi.org/10.1017/S0022112067002605
[6]	Benjamin, T.B., Bona, J.L. and Mahony, J.J. (1972) Model Equations for Long Waves in Nonlinear Dispersive Systems. Philosophical Transactions of the Royal Society London Series A, 272, 47-78. http://dx.doi.org/10.1098/rsta.1972.0032
[7]	Bibi, S. and Mohyud-Din, S.T. (2014) Traveling Wave Solutions of ZK-BBM Equation Sine-Cosine Method. Communications in Numerical Analysis, 2014, Article ID: cna-00154.
[8]	Gupta, R.K., Kumar, S. and Lal, B. (2012) New Exact Travelling Wave Solutions of Generalised sinh-Gordon and (2+1)-Dimensional ZK-BBM Equations. Maejo International Journal of Science and Technology, 6, 344-355.
[9]	Wazwaz, A.-M. (2005) Compact and Noncompact Physical Structures for the ZK-BBM Equation. Applied Mathematics and Computation, 169, 713-725. http://dx.doi.org/10.1016/j.amc.2004.09.062
[10]	Wazwaz, A.-M. (2008) The Extended tanh Method for New Compact and Noncompact Solutions for the KP-BBM and the ZK-BBM Equations. Chaos, Solitons and Fractals, 38, 1505-1516. http://dx.doi.org/10.1016/j.chaos.2007.01.135