分离变量法求解一些非线性发展方程的显式解  

Explicit Solutions of Some Nonlinear Evolution Equations through Separation of Variables

作　　者：王凡凡 江志松 WANG Fanfan;JIANG Zhisong(School of Mathematics,East China University of Science and Technology,Shanghai 200237,China)

机构地区：[1]华东理工大学数学学院,上海200237

出　　处：《大学数学》2024年第2期58-62,共5页College Mathematics

基　　金：国家自然科学基金资助项目(11102068,11302182);上海市重点建设课程(高等数学)项目(2020)。

摘　　要：利用分离变量法求解一些非线性发展方程,如Harry-Dym方程,Hunter-Saxton方程,非线性扩散方程,半经典极限KdV方程等方程新的显式解析解.有意思的是,贝塞尔函数出现在部分解的表达式中,有些解可以预测解的爆破现象.The method of separation of variables is used to solve some nonlinear evolution equations such as the Harry-Dym equation,the extended Harry-Dym equation,the Hunter-Saxton equation,the nonlinear diffusion equation,the semi-classical limit KdV and mKdV equations and others,by which new explicit solutions of these nonlinear evolution equations are obtained.Interestingly,Bessel functions appear in these solutions.Some of the solutions also give the prediction of blow-up phenomenon.

关 键 词：分离变量法 非线性发展方程 显式解 

分 类 号：O175.24[理学—数学]