A refined invariant subspace method and applications to evolution equations  

作　　者：MA Wen-Xiu 

机构地区：[1]Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA

出　　处：《Science China Mathematics》2012年第9期1769-1778,共10页中国科学：数学（英文版）

基　　金：supported by the State Administration of Foreign Experts Affairs of China,National Natural Science Foundation of China (Grant Nos. 10971136,10831003,61072147,11071159);Chunhui Plan of the Ministry of Education of China,Zhejiang Innovation Project (Grant No. T200905);the Natural Science Foundation of Shanghai and the Shanghai Leading Academic Discipline Project (Grant No.J50101)

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 oi1 the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differentii equations and their corresponding exact solutions with generalized separated variables.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.

关 键 词：invariant subspace generalized separation of variables evolution equation 

分 类 号：O175.29[理学—数学] O177.1[理学—基础数学]