New invariant surface measures for the cubic Schr\"odinger equation

TL;DR

This paper introduces new invariant measures for the cubic defocusing nonlinear Schr"odinger equation in one and two dimensions, supported on specific mass level sets, advancing the understanding of its long-term behavior.

Contribution

It constructs novel invariant measures supported on mass level sets for the cubic Schr"odinger equation in 1D and 2D, a new approach in the study of its dynamics.

Findings

Invariant measures supported on mass level sets

Applicable to 1D and 2D cubic Schr"odinger equations

Enhances understanding of long-term dynamics

Abstract

We construct new invariant measures supported on mass level sets for the cubic defocusing nonlinear Schr\"odinger equation in dimensions $1$ and $2$.