Hamiltonian description and traveling waves of the spatial Dysthe equations
Résumé
The spatial version of the fourth-order Dysthe equations describe the evolution of the wave envelope and potential of the wave-induced mean flow in deep waters. The hidden Hamiltonian structure and new invariants are unveiled by means of a gauge transformation to a new canonical form of the evolution equations. A highly accurate Fourier-type spectral scheme is developed to solve for the equations and validate the new conservation laws, which are satisfied up to machine precision. Further, traveling waves are numerically investigated using the Petviashvili method. It is found that their collision appears inelastic, suggesting the non-integrability of the Dysthe equations.
Domaines
Mécanique des fluides [physics.class-ph] Mécanique des fluides [physics.class-ph] Formation de Structures et Solitons [nlin.PS] Systèmes Solubles et Intégrables [nlin.SI] Analyse numérique [math.NA] Equations aux dérivées partielles [math.AP] Physique Numérique [physics.comp-ph] Physique Atmosphérique et Océanique [physics.ao-ph] Dynamique des Fluides [physics.flu-dyn]
Origine : Fichiers produits par l'(les) auteur(s)