KAM for reversible derivative wave equations

TL;DR

This paper proves the existence of small amplitude, quasi-periodic solutions for derivative wave equations using a KAM theorem, showing these solutions are stable and reducible to constant coefficients.

Contribution

It introduces an abstract KAM theorem tailored for infinite dimensional reversible systems, establishing the existence of stable quasi-periodic solutions in derivative wave equations.

Findings

Existence of Cantor families of solutions

Solutions have zero Lyapunov exponents

Linearized equations are reducible to constant coefficients

Abstract

We prove the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. This result is derived by an abstract KAM theorem for infinite dimensional reversible dynamical systems