Large deviations principle for the cubic NLS equation
Analysis of PDEs
2021-11-16 v2 Probability
Abstract
In this paper, we present a probabilistic study of rare phenomena of the cubic nonlinear Schr\"odinger equation on the torus in a weakly nonlinear setting. This equation has been used as a model to numerically study the formation of rogue waves in deep sea. Our results are twofold: first, we introduce a notion of criticality and prove a Large Deviations Principle (LDP) for the subcritical and critical cases. Second, we study the most likely initial conditions that lead to the formation of a rogue wave, from a theoretical and numerical point of view. Finally, we propose several open questions for future research.
Cite
@article{arxiv.2110.15748,
title = {Large deviations principle for the cubic NLS equation},
author = {Miguel Angel Garrido and Ricardo Grande and Kristin M. Kurianski and Gigliola Staffilani},
journal= {arXiv preprint arXiv:2110.15748},
year = {2021}
}