A refined invariant subspace method and applications to evolution equations

被引：108
作者：
Ma Wen-Xiu [1 ]
机构：
[1] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA
来源：
SCIENCE CHINA-MATHEMATICS | 2012年 / 55卷 / 09期
基金：
中国国家自然科学基金; 上海市自然科学基金;
关键词：
invariant subspace; generalized separation of variables; evolution equation; LIE-BACKLUND SYMMETRIES; DE-VRIES EQUATION; COMPLEXITON SOLUTIONS; BOUSSINESQ EQUATION; DIFFUSION-EQUATIONS; WRONSKIAN SOLUTIONS; REDUCTION;
D O I：
10.1007/s11425-012-4408-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations is analyzed to shed light on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.
引用
收藏
页码：1769 / 1778
页数：10
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