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

Recurrence in the high-order nonlinear Schrödinger equation: A low-dimensional analysis We study a three-wave truncation of the high-order nonlinear Schrödinger equation for deep-water waves (also named Dysthe equation). We validate the model by comparing it to numerical simulation; we 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review E American Physical Society (APS)

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

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

Abstract

We study a three-wave truncation of the high-order nonlinear Schrödinger equation for deep-water waves (also named Dysthe equation). We validate the model by comparing it to numerical simulation; we 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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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1539-3755
eISSN
550-2376
D.O.I.
10.1103/PhysRevE.96.012222
Publisher site
See Article on Publisher Site

Abstract

We study a three-wave truncation of the high-order nonlinear Schrödinger equation for deep-water waves (also named Dysthe equation). We validate the model by comparing it to numerical simulation; we 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.

Journal

Physical Review EAmerican Physical Society (APS)

Published: Jul 26, 2017

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