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arXiv · 1703.09482

Recurrence in the high-order nonlinear Schrödinger equation: a low dimensional analysis

Andrea Armaroli·Maura Brunetti·Jérôme Kasparian
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Abstract

We study a three-wave truncation of the high-order nonlinear Schrödinger 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.

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Andrea Armaroli, Maura Brunetti, Jérôme Kasparian. 2017-07-25. Recurrence in the high-order nonlinear Schrödinger equation: a low dimensional analysis. https://doi.org/10.1103/physreve.96.012222

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