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arXiv · 1307.5507

Some special solutions to the Hyperbolic NLS equation

Laurent Vuillon·Denys Dutykh·Francesco Fedele
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Abstract

The Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili method is exploited to numerically compute bi-periodic time-harmonic solutions of the HypNLS equation. In physical space they represent non-localized standing waves. Non-trivial spatial patterns are revealed and an attempt is made to describe them using symbolic dynamics and the language of substitutions. Finally, the dynamics of a slightly perturbed standing wave is numerically investigated by means a highly acccurate Fourier solver.

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BibTeXRIS

Laurent Vuillon, Denys Dutykh, Francesco Fedele. 2013-07-21. Some special solutions to the Hyperbolic NLS equation. https://doi.org/10.1016/j.cnsns.2017.09.018

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