On a large deviation principle for 1d cubic NLS with optimal decaying data

TL;DR

This paper establishes large deviation principles for one-dimensional cubic nonlinear Schrödinger equations with initial data that has optimal polynomial decay, extending previous results to more general random initial conditions.

Contribution

It generalizes existing large deviation results for cubic NLS by considering initial data with optimal polynomial decay in Fourier coefficients.

Findings

Proves large deviation principles for a broader class of initial data.

Extends previous work to include more general random initial conditions.

Demonstrates the applicability of large deviation techniques to cubic NLS with optimal decay.

Abstract

In this article, we revisit the work of \cite{garrido2023large}, and prove large deviation principles for more general random initial data for cubic NLS. The Fourier coefficient of our random data admits an optimal polynomial decay.