Long time stability of KAM tori for nonlinear wave equation

TL;DR

This paper proves the long-term stability of KAM tori for nonlinear wave equations by constructing a higher-order partial normal form and demonstrating the persistence of the p-tame property through iterative procedures.

Contribution

It introduces a method to establish long-time stability of KAM tori in infinite-dimensional Hamiltonian systems via advanced normal form techniques.

Findings

KAM tori are stable over long times in nonlinear wave equations.

p-tame property remains intact through KAM and normal form iterations.

Constructs a higher-order partial normal form around the KAM torus.

Abstract

It is proved that the KAM tori (thus quasi-periodic solutions) are long time stable for infinite dimensional Hamiltonian systems generated by nonlinear wave equation, by constructing a partial normal form of higher order around the KAM torus and showing $p$-tame property persists under KAM iterative procedure and normal form iterative procedure.