On almost periodic solutions to NLS without external parameters

TL;DR

This paper discusses the existence of many infinite-dimensional almost periodic solutions for nonlinear Schrödinger equations on the circle without external parameters, highlighting new proof techniques.

Contribution

It provides an extended sketch of the proof for the existence of non-resonant invariant tori in NLS without external parameters, emphasizing novel methodological points.

Findings

Existence of infinitely many non-resonant invariant tori

Presence of numerous almost periodic solutions

Extension of previous results with new proof insights

Abstract

In this note, we present a result established in [BGR24] where we prove that nonlinear Schrodinger equations on the circle, without external parameters, admit plenty of infinite dimensional non resonant invariant tori, or equivalently, plenty of almost periodic solutions. Our aim is to propose an extended sketch of the proof, emphasizing the new points which have enabled us to achieve this result.