Some special solutions to the Hyperbolic NLS equation

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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  • HAL Id : hal-00846801, version 2
  • ARXIV : 1307.5507

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Laurent Vuillon, Denys Dutykh, Francesco Fedele. Some special solutions to the Hyperbolic NLS equation. 25 pages, 10 figures, 56 references. Other author's papers can be found at http://www.denys-dutyk.. 2014. <hal-00846801v2>

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