摘要
在齐次平衡法和辅助方程法的基础上,引入两种函数变换,把二阶线性偏微分方程转化为二阶常系数线性常微分方程,并通过讨论常微分方程的解来构造一些非线性发展方程的精确解.借助符号计算系统Math-ematica,构造了非线性长波方程新的复合型精确解,验证了方法的有效性.
Based on homogenous balance method and auxiliary equation method,two kinds of function transformation are introduced to change a second order linear partial differential equation into a second order linear ordinary differential equation with constant coefficients.A number of exact solutions to nonlinear evolution equations are constructed by using the solutions of the ordinary differential equation.To illustrate the method,the nonlinear long wave equation is chosen to construct the new exact complex solutions with the help of symbolic computation system Mathematica.
出处
《内蒙古师范大学学报（自然科学汉文版）》
CAS
2009年第6期611-615,622,共6页
Journal of Inner Mongolia Normal University(Natural Science Edition)
基金
国家自然科学基金资助项目(10761005)
内蒙古自然科学基金资助项目(200408020103)
内蒙古自治区高等学校科学研究基金资助项目(NJZZ07031)
内蒙古师范大学自然科学基金资助项目(QN005023)
关键词
非线性长波方程
复合型精确解
齐次平衡法
辅助方程法
函数变换
homogenous balance method
auxiliary equation method
nonlinear evolution equation
exact complex solution
