摘要
Camassa和Holm于1993年推导出了具有尖峰孤立波解的CH方程.尖峰孤立波解引起了数学物理学家的广泛关注,而且获得了多个此类精确解.为了构造非线性发展方程的无穷序列尖峰孤立波解,本文给出了一种辅助方程的Bcklund变换和解的非线性叠加公式,并借助符号计算系统Mathematica,构造了CH-r方程的无穷序列尖峰孤立波解.
Camssa and Holm derived in 1993 the CH equation and obtained its peak solitary wave solutions, then many mathematicians and physicians have studied the peak solitary wave solutions and found finite exact solutions. In the paper, to construct an infinite sequence of peak solitary wave solutions of nonlinear evolution equations, we present the B/icklund transformation of an auxiliary equation and nonlinear superposition formula of the solutions to find an infinite sequence of peak solitary wave solutions to the CH-r equation with the help of the symbolic computation system in Mathematica.
出处
《工程数学学报》
CSCD
北大核心
2012年第6期865-876,共12页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(10862003)
内蒙古自治区自然科学基金(2010MS0111)
内蒙古自治区高等学校科学研究基金(NJZY12031)~~
关键词
辅助方程
解的非线性叠加公式
CH-r方程
尖峰孤立波解
auxiliary equation
nonlinear superposition formula of the solutions
CH-r equation
peak solitary wave solution
