量子电子学报, 2016, 33 (6): 680, 网络出版: 2017-01-03
基于exp[-φ(ξ)]-展开法求变系数 非线性发展方程的精确解
Exact solutions of nonlinear evolution equations with variable coefficients based onexp[-φ(ξ)]-expansion method
摘要
exp[-φ(ξ)]-展开法可用于求解变系数非线性发展方程,以广义变系数KdV-mKdV方程 和变系数(2+1)维Broer-Kaup方 程组为例实现了求解过程,获得了奇异行波解,包括指数函数解、双曲函数解、三角函数解及有 理函数解,并通过取特殊值得到结(kink)型解。可见exp[-φ(ξ)]-展开法适于变系数非线性发展方程的求解,且更具一般性。
Abstract
The exp[-φ(ξ)]-expansion method can be used to solve the nonlinear evolution equation with variable coefficients. By taking the generalized variable coefficient KdV-mKdV equation and variable coefficient (2+1)-dimensional Broer-Kaup equations as an example, the solving process is realized and singular travelling wave solutions are obtained, which are expressed in terms of the exponential functions, hyperbolic functions, trigonometric functions and rational functions. When parameters are taken to be special values, the kink type solitary wave solutions are derived. It is shown that the exp[-φ(ξ)]-expansion method is suitable for solving the nonlinear evolution equations with variable coefficients, and it is more general.
王晓利, 斯仁道尔吉. 基于exp[-φ(ξ)]-展开法求变系数 非线性发展方程的精确解[J]. 量子电子学报, 2016, 33(6): 680. WANG Xiaoli, Sirendaoerji. Exact solutions of nonlinear evolution equations with variable coefficients based onexp[-φ(ξ)]-expansion method[J]. Chinese Journal of Quantum Electronics, 2016, 33(6): 680.