Invariant tori for commuting Hamiltonian PDEs

Details Invariant tori for commuting Hamiltonian PDEs Invariant tori for commuting Hamiltonian PDEs

2008-05-18

arxiv.org/abs/0805.2758v1

Mathematics

Functional Analysis

Scientific paper

We generalize to some PDEs a theorem by Nekhoroshev on the persistence of invariant tori in Hamiltonian systems with $r$ integrals of motion and $n$ degrees of freedom, $r\leq n$. The result we get ensures the persistence of an $r$-parameter family of $r$-dimensional invariant tori. The parameters belong to a Cantor-like set. The proof is based on the Lyapunof-Schmidt decomposition and on the standard implicit function theorem. Some of the persistent tori are resonant. We also give an application to the nonlinear wave equation with periodic boundary conditions on a segment and to a system of coupled beam equations. In the first case we construct 2 dimensional tori, while in the second case we construct 3 dimensional tori.

Affiliated with

Also associated with

No associations

Rating

Invariant tori for commuting Hamiltonian PDEs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Invariant tori for commuting Hamiltonian PDEs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Invariant tori for commuting Hamiltonian PDEs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-647546