Stable and unstable time quasi periodic solutions for a system of coupled NLS equations

TL;DR

This paper demonstrates the existence of both stable and unstable small KAM tori in a coupled nonlinear Schrödinger system on the torus, highlighting the first example of unstable tori in a 1D PDE and linking instability to beating phenomena.

Contribution

It provides the first example of unstable tori in a 1D PDE and connects their instability to beating phenomena, expanding understanding of dynamics in coupled NLS systems.

Findings

Existence of stable and unstable small KAM tori in the system

Unstable tori are related to beating phenomena

First example of unstable tori in a 1D PDE

Abstract

We prove that a system of coupled nonlinear Schr{\"o}dinger equations on the torus exhibits both stable and unstable small KAM tori. In particular the unstable tori are related to a beating phenomena which has been proved recently in [6]. This is the first example of unstable tori for a 1d PDE.