Invariant tori for 1D quintic nonlinear wave equation

[摘要] In this paper, one-dimensional (1D) nonlinear wave equation u(tt) - u(xx) + mu + u(5) = 0 on the finite x-interval [0, pi] with Dirichlet boundary conditions is considered. It is proved that, for any integer b >= 2, there are many b-dimensional elliptic invariant tori, and thus quasi-periodic solutions for the above equation. This is an extension of the previous work [6] by the same authors, where b = 2. The proof is based on infinite dimensional KAM theory and partial Birkhoff normal form. (C) 2017 Elsevier Inc. All rights reserved.

[发布日期] 2017-12-15