Recurrence in the high-order nonlinear Schr\"odinger equation: a low dimensional analysis

Andrea Armaroli; J\'er\^ome Kasparian; Maura Brunetti

arxiv: 1703.09482 · v2 · pith:RASMBRAInew · submitted 2017-03-28 · ⚛️ physics.flu-dyn · nlin.PS

Recurrence in the high-order nonlinear Schr\"odinger equation: a low dimensional analysis

Andrea Armaroli , Maura Brunetti , J\'er\^ome Kasparian This is my paper

classification ⚛️ physics.flu-dyn nlin.PS

keywords equationnonlinearhigh-orderodingerschraccordingallowsanalysis

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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.

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