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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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Laurent Vuillon, Denys Dutykh, Francesco Fedele. Some special solutions to the Hyperbolic NLS equation. Communications in Nonlinear Science and Numerical Simulation, Elsevier, 2018, 57, pp.202-220. ⟨10.1016/j.cnsns.2017.09.018⟩. ⟨hal-00846801v3⟩

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