# A KAM Theorem for Higher Dimensional Reversible Nonlinear Schr\"{o}dinger Equations

## TL;DR

This paper establishes a KAM theorem for infinite-dimensional reversible systems and demonstrates the existence and stability of quasi-periodic solutions for certain nonlinear Schrödinger equations on multi-dimensional tori.

## Contribution

It introduces a new KAM theorem applicable to infinite-dimensional reversible systems, enabling analysis of nonlinear Schrödinger equations beyond Hamiltonian cases.

## Key findings

- Existence of quasi-periodic solutions for nonlinear Schrödinger systems.
- Linear stability of these solutions.
- Extension of KAM theory to reversible, non-Hamiltonian systems.

## Abstract

In the paper, we prove an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible systems. Using this KAM theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of reversible (non-Hamiltonian) coupled nonlinear Schr\"{o}dinger systems on $d-$torus $\mathbb{T}^d$.