KAM theory for the Hamiltonian derivative wave equation

TL;DR

This paper proves an infinite-dimensional KAM theorem demonstrating the existence of Cantor families of small-amplitude, invariant tori in Hamiltonian derivative wave equations, advancing the understanding of their long-term dynamics.

Contribution

It introduces a new infinite-dimensional KAM theorem specifically for Hamiltonian derivative wave equations, establishing the existence of invariant tori.

Findings

Existence of Cantor families of invariant tori in Hamiltonian derivative wave equations

Small-amplitude, reducible, elliptic, analytic invariant tori are proven to exist

Advances the understanding of stability and long-term behavior in these equations

Abstract

We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations