摘要
为了获得变系数非线性发展方程的无穷序列精确解,给出一种辅助方程的Bcklund变换,并用符号计算系统Mathematica构造了广义变系数KdV方程和带强迫项变系数组合KdV方程的无穷序列精确解.这里包括无穷序列光滑孤立子解和无穷序列尖峰孤立子解.这种方法在寻找其他变系数非线性发展方程无穷序列精确解方面具有普遍意义.
In order to obtain an infinite sequence of exact solutions to nonlinear evolution equations with variable coefficients, Backlund transformation of auxiliary equations is given,and the infinite sequence of exact solutions to the general variable coefficient KdV equation and variable coefficient combined KdV equation with forced terms are obtained with the help of symbolic computation system Mathematica. The solutions include the infinite sequence of smooth soliton solutions and infinite sequence of peaked soliton solutions. It is of significance to seek an infinite sequence of exact solutions to other nonlinear evolution equations with variable coefficients.
出处
《内蒙古大学学报（自然科学版）》
CAS
CSCD
北大核心
2011年第4期367-375,共9页
Journal of Inner Mongolia University：Natural Science Edition
基金
内蒙古自治区高等学校科学研究基金资助项目(批准号:NJZZ07031)
内蒙古自治区自然科学基金资助项目(批准号:2010MS0111)
关键词
辅助方程法
Bcklund变换
无穷序列精确解
变系数非线性发展方程
auxiliary equation method
Backlund transformation
infinite sequence of exact solution
variable coefficient nonlinear evolution equation
