Maximal Dimension of Invariant Subspaces to Systems of Nonlinear Evolution Equations  

作　　者：Shoufeng SHEN Changzheng QU Yongyang JIN Lina JI 

机构地区：[1]Department of Applied Mathematics,Zhejiang University of Technology,Hangzhou 310023,China [2]Department of Mathematics,Ningbo University,Ningbo 315211,Zhejiang,China [3]Department of Information and Computational Science,Henan Agricultural University,Zhengzhou 450002,China

出　　处：《Chinese Annals of Mathematics,Series B》2012年第2期161-178,共18页数学年刊（B辑英文版）

基　　金：Project supported by the National Natural Science Foundation of China for Distinguished Young Scholars (No.10925104);the National Natural Science Foundation of China (No.11001240);the Doctoral Program Foundation of the Ministry of Education of China (No.20106101110008);the Zhejiang Provincial Natural Science Foundation of China (Nos.Y6090359,Y6090383)

摘　　要：In this paper, the dimension of invariant subspaces admitted by nonlinear sys- tems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator F = （F1, F2） with orders {k1, k2} （k1≥ k2） preserves the invariant subspace Wn1^1× Wn2^2 （n1 ≥ n2）, then n1 - n2 ≤ k2, n1 ≤2（k1 ＋ k2） ＋ 1, where Wnq^q is the space generated by solutions of a linear ordinary differential equation of order nq （q = 1, 2）. Several examples including the （1＋1）-dimensional diffusion system and Ito＇s type, Drinfel＇d-Sokolov-Wilson＇s type and Whitham-Broer-Kaup＇s type equations are presented to illustrate the result. Furthermore, the estimate of dimension for m-component nonlinear systems is also given.

关 键 词：Invariant subspace Nonlinear PDEs Exact solution SYMMETRY Dynamical system 

分 类 号：O175.29[理学—数学] V474.2[理学—基础数学]