Infinite dimensional invariant tori for nonlinear Schr\"odinger equations
Analysis of PDEs
2025-02-13 v2 Dynamical Systems
Abstract
We prove that nonlinear Schr\"odinger equations on the circle, without external parameters, admits plenty of almost periodic solutions. Indeed, we prove that arbitrarily close to most of the finite dimensional KAM tori constructed by Kuksin--Poschel in 1996, there exist infinite dimensional non resonant Kronecker tori, i.e. rotational invariant tori. This result answers a natural and longstanding question, well identified by the Hamiltonian PDE community since the first KAM-type result for PDEs by Kuksin in 1987.
Keywords
Cite
@article{arxiv.2412.11845,
title = {Infinite dimensional invariant tori for nonlinear Schr\"odinger equations},
author = {Joackim Bernier and Benoit Grébert and Tristan Robert},
journal= {arXiv preprint arXiv:2412.11845},
year = {2025}
}