摘要
本文以数学机械化思想为指导,以计算机代数系统软件Maple为工具,提出了用扩展的F-展法来构造非线性孤子方程的行波解.为了验证方法的有效性和优越性,将其应用到耦合的KdV方程,获得了具有一般形式的新的精确解,其中包括单的和耦合的Jacobi椭圆函数解、类孤子解及三角函数解.
The thesis improves the F - expansion method for constructing travelling wave solutions of nonlinear soliton equations under the guidance of mathematics mechanization and with the tools of transformation and computer algebraic system Maple. In order to illus- trate the effectiveness and advantages of the method, the study applies it to the coupled KdV equations. Many new and general formal ex- act solutions for the coupled KdV equations are obtained including the single and combined Jacobi elliptic function solutions, soliton - like solutions, trigonometric function solutions.
作者
于义
YU Yi （Fushun Teachers College, Fushun Liaoning 113001, China）
关键词
孤子方程
精确解
F-展开法
Soliton equations
Exact solutions
F - expansion method
