Supercritical Nonlinear Schr\"odinger equations: Quasi-Periodic Solutions

TL;DR

This paper develops a novel method to construct time quasi-periodic solutions for supercritical nonlinear Schrödinger equations on multi-dimensional tori, expanding the understanding of such complex dynamical systems.

Contribution

It introduces a new approach for constructing quasi-periodic solutions to supercritical NLS equations, applicable in arbitrary dimensions.

Findings

Successfully constructs quasi-periodic solutions in supercritical regimes.

Proposes a new general approach with potential broader applications.

Extends previous work to higher dimensions and energy regimes.

Abstract

We construct time quasi-periodic solutions to the energy supercritical nonlinear Schr\"odinger equations on the torus in arbitrary dimensions. This introduces a new approach, which could have general applicability.