Recurrence in the high-order nonlinear Schr\"odinger equation: a low dimensional analysis
Fluid Dynamics
2017-08-02 v2 Pattern Formation and Solitons
Abstract
We study a three-wave truncation of the high-order nonlinear Schr\"odinger equation for deepwater waves (HONLS, also named Dysthe equation). We validate our approach by comparing it to numerical simulation, distinguish the impact of the different fourth-order terms and classify the solutions according to their topology. This allows us to properly define the temporary spectral upshift occurring in the nonlinear stage of Benjamin-Feir instability and provides a tool for studying further generalizations of this model.
Cite
@article{arxiv.1703.09482,
title = {Recurrence in the high-order nonlinear Schr\"odinger equation: a low dimensional analysis},
author = {Andrea Armaroli and Maura Brunetti and Jérôme Kasparian},
journal= {arXiv preprint arXiv:1703.09482},
year = {2017}
}