Some special solutions to the Hyperbolic NLS equation
Résumé
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.
Domaines
Mécanique des fluides [physics.class-ph] Mécanique des fluides [physics.class-ph] Milieux et Changements globaux Analyse numérique [math.NA] Equations aux dérivées partielles [math.AP] Formation de Structures et Solitons [nlin.PS] Dynamique des Fluides [physics.flu-dyn] Physique Atmosphérique et Océanique [physics.ao-ph] Physique Numérique [physics.comp-ph] Systèmes Solubles et Intégrables [nlin.SI] Géophysique [physics.geo-ph] Géophysique [physics.geo-ph]| Origine | Fichiers produits par l'(les) auteur(s) |
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