TITLE

Maximal dimension of invariant subspaces to systems of nonlinear evolution equations

AUTHOR(S)
Shen, Shoufeng; Qu, Changzheng; Jin, Yongyang; Ji, Lina
PUB. DATE
March 2012
SOURCE
Chinese Annals of Mathematics;Mar2012, Vol. 33 Issue 2, p161
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, the dimension of invariant subspaces admitted by nonlinear systems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator $\mathbb{F} = (F^1 ,F^2 )$ with orders { k, k} ( k ≥ k) preserves the invariant subspace $W_{n_1 }^1 \times W_{n_2 }^2 (n_1 \geqslant n_2 )$, then n − n ≤ k, n ≤ 2( k + k) + 1, where $W_{n_q }^q $ is the space generated by solutions of a linear ordinary differential equation of order n ( q = 1, 2). Several examples including the (1+1)-dimensional diffusion system and Itô'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.
ACCESSION #
72900004

 

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