# Reducibility of linear quasi-periodic Hamiltonian derivative wave equations and half-wave equations under the Brjuno conditions

## TL;DR

This paper extends KAM theory to prove the reducibility of certain linear quasi-periodic Hamiltonian PDEs, specifically derivative wave and half-wave equations, under Brjuno conditions, broadening the scope of Hamiltonian system analysis.

## Contribution

It generalizes KAM theory from finite-dimensional systems to infinite-dimensional Hamiltonian PDEs under Brjuno non-resonance conditions.

## Key findings

- Proves reducibility of derivative wave equations.
- Establishes reducibility of half-wave equations.
- Extends KAM theory to Hamiltonian PDEs.

## Abstract

In this paper, we prove the reducibility for some linear quasi-periodic Hamiltonian derivative wave and half-wave equations under the Brjuno-R\"{u}ssmann non-resonance conditions. This generalizes KAM theory by P\"{o}schel in [38] from the finite dimensional Hamiltonian systems to Hamiltonian PDEs.