Quasi-periodic solutions for 1D wave equation with the nonlinearity u2p+1

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:410

Article

Gao, Meina

关键词: Quasi-periodic solutions;    Infinite-dimensional KAM theory;    Partial Birkhoff normal form;   

DOI  :  10.1016/j.jmaa.2013.08.066

来源: Elsevier

【 摘 要 】

In this paper, one-dimensional (1D) nonlinear wave equation u(tt) - u(xx) + mu + u(2p+1) = 0, p is an element of N, on the finite x-interval [0, pi] with Dirichlet boundary conditions is considered. It is proved that there are many 2-dimensional elliptic invariant tori, and thus quasi-periodic solutions for the above equation. The proof is based on infinite-dimensional KAM theory and partial Birkhoff normal form. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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