Application of Trial Equation Method for Solving the Getmanou Equation

Li Yang

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

DOI: 10.4236/am.2014.510139                

Abstract

Under the travelling wave transformation, some nonlinear partial differential equations such as the Getmanou equation are transformed to ordinary differential equation. Then using trial equation method and combing complete discrimination system for polynomial, the classifications of all single traveling wave solution to this equation are obtained.

Keywords

trialequation method, the Getmanou equation, complete discrimination system for polynomial, the nonlinear partial differential equation, traveling wave transform

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Ablowitz, M.J. and Clarkson, P.A. (1992) Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, Cambridge, 721-725.
[2]	Satsuma, J. and Kaup D.J. (1977) A Backlund Transformation for a Higher Order Korteweg-De Vries Equation. Journal of the Physical Society of Japan, 43, 692-697. http://dx.doi.org/10.1143/JPSJ.43.692
[3]	Gu, C., Hu, H. and Zhou, Z. (2006) Darboux Transformations in Integrable Systems: Theory and Their Applications to Geometry. Springer, Berlin, Heidelberg.
[4]	Wang, M., Zhou, Y. and Li, Z. (1996) Application of a Homogeneous Balance Method to Exact Solutions of Nonlinear Equations in Mathematical Physics. Physics Letters A, 216, 67-75. http://dx.doi.org/10.1016/0375-9601(96)00283-6
[5]	Fan, E. (2000) Extended tanh-Function Method and Its Applications to Nonlinear Equations. Physics Letters A, 277, 212-218. http://dx.doi.org/10.1016/S0375-9601(00)00725-8
[6]	He, J.H. and Zhang, L.N. (2008) Generalized Solitary Solution and Compacton-Like Solution of the Jaulent—Miodek Equations Using the Exp-Function Method. Physics Letters A, 372, 1044-1047. http://dx.doi.org/10.1016/j.physleta.2007.08.059
[7]	Wang, M., Li, X. and Zhang, J. (2008) The (G'/G)-Expansion Method and Travelling Wave Solutions of Nonlinear Evolution Equations in Mathematical Physics. Physics Letters A, 372, 417-423. http://dx.doi.org/10.1016/j.physleta.2007.07.051
[8]	Liu, C.S. (2006) Trial Equation Method to Nonlinear Evolution Equations with Rank Inhomogenous: Mathematical Discussions and Its Applications. Communications in Theoretical Physics, 45, 219-223. http://dx.doi.org/10.1088/0253-6102/45/2/005
[9]	Liu, C.S. (2005) Trial Equation Method and Its Applications to Nonlinear Evolution Equations. Acta Physica Sinica, 54, 2505. (in Chinese)
[10]	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
[11]	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/ 0609058.
[12]	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, 291296. http://dx.doi.org/10.1088/0253-6102/49/2/07
[13]	Fan, X.-F. (2010) Classification of All Single Traveling-Wave Solutions to Getmanou Equation. FIZIKA A, 19, 191196.