| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 5011273 | Communications in Nonlinear Science and Numerical Simulation | 2018 | 19 Pages |
Abstract
The Hyperbolic Nonlinear Schrödinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrow-band deep water gravity waves. In this study, the symmetries and conservation laws of this equation are computed. The Petviashvili method is then 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 accurate Fourier solver.
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Authors
Laurent Vuillon, Denys Dutykh, Francesco Fedele,