English

A KAM theorem with applications to partial equations of higher dimension

Dynamical Systems 2009-11-11 v1 Mathematical Physics math.MP

Abstract

The existence of lower dimensional KAM tori is shown for a class of nearly integrable Hamiltonian systems where the second Melnikov's conditions are eliminated. As a consequence, it is proved that there exist many invariant tori and thus quasi-periodic solutions for nonlinear wave equations, Schr\"odinger equations and other equations of higher spatial dimension.

Keywords

Cite

@article{arxiv.math/0606459,
  title  = {A KAM theorem with applications to partial equations of higher dimension},
  author = {Xiaoping Yuan},
  journal= {arXiv preprint arXiv:math/0606459},
  year   = {2009}
}