Lan K L, Wang H B. Exact solutions for two nonlinear equations: I[J]. J Phys,1990,A23:3923-3928.
[4]
Parkes E J, Duffy B R. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations[J]. Comput Phys Commun,1996,98:288-300.
[5]
Fu Z T, Liu S K, Liu S D. New exact solutions to the KdV-Burgers-Kuramoto equation[J]. Chaos Soliton Fract,2005,23:609-616.
[6]
Zhang S. New exact solutions of the KdV-Burgers-Kuramoto equation[J]. Phys Lett,2006,A358:414-420.
[7]
Khuri S A. Traveling wave solutions for nonlinear differential equations: a unified Ans？tze approach[J]. Chaos Soliton Fract,2007,32:252-258.
[8]
Olver P J. Application of Lie Groups to Differential Equations[M]. New York:Springer-Verlag,1986. Series Solutions of a Type of Nonlinear Evolution Equation LIU Qian1, ZHOU Yu-qian2, DU Xian-yun3 (1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, Sichuan; 2. College of Computer Science and Technology, Southwest University for Nationalities, Chengdu 610041, Sichuan; 3. College of Mathematics, Chengdu University of Information Technology, Chengdu 610225, Sichuan) Abstract:In this paper, the Lie symmetry method is performed on a type of nonlinear evolution equation, the finite dimensional Lie symmetry is obtained. Furthermore, by the adjoint representation, the one dimensional optimal system is constructed. Based on it, four types of reduced systems and the corresponding group-invariant solutions including the power series solutions are obtained. Key words:nonlinear evolution equation; optimal system; series solution 2000 MSC:35Q20; 35Q53
[9]
Liu S D, Liu S K, Huang Z H, et al. On a class of nonlinear Schr？dinger equations III[J]. Prog Natural Sci,1999,9:912-918.
