Construction of Quasi-periodic solutions with the same Gevrey index as nonlinear terms in Multi-Dimensional NLS

TL;DR

This paper proves the existence of Gevrey smooth quasi-periodic solutions in multi-dimensional nonlinear Schrödinger equations, matching the Gevrey index of the nonlinearity, using the Craig-Wayne-Bourgain method.

Contribution

It demonstrates the construction of quasi-periodic solutions with the same Gevrey index as the nonlinear terms in multi-dimensional NLS, extending previous results to a broader class of nonlinearities.

Findings

Existence of Gevrey smooth quasi-periodic solutions

Solutions share the same Gevrey index as the nonlinearity

Application of Craig-Wayne-Bourgain method to multi-dimensional NLS

Abstract

We investigate the persistency of quasi-periodic solutions to multi-dimensional nonlinear Schr\"{o}dinger equations (NLS) involving Gevrey smooth nonlinearity with an arbitrary Gevrey index $\alpha>1$. By applying the Craig-Wayne-Bourgain (CWB) method, we establish the existence of quasi-periodic solutions that are Gevrey smooth with the same Gevrey index as the nonlinearity.