Invariant tori for 1D quintic nonlinear wave equation.

In this paper, one-dimensional (1D) nonlinear wave equation u t t − u x x + m u + u 5 = 0 on the finite x -interval [ 0 , π ] 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. [ABSTRACT FROM AUTHOR]