On the construction of Sobolev Almost periodic invariant tori for the 1d NLS

TL;DR

This paper introduces a novel method for constructing Sobolev almost periodic invariant tori in the 1D nonlinear Schrödinger equation, marking the first such result for PDEs with Sobolev regularity.

Contribution

It presents the first construction of Sobolev almost periodic solutions for PDEs, specifically for the 1D analytic NLS.

Findings

Constructed Sobolev almost periodic invariant tori for 1D NLS.

Established a new method applicable to PDEs with Sobolev regularity.

First such result for PDEs with these properties.

Abstract

We discuss a method for the construction of almost periodic solutions of the one dimensional analytic NLS with only Sobolev regularity both in time and space. This is the first result of this kind for PDEs.