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| HAL : hal-00687325, version 3 |
| arXiv : 1204.2889 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (13-04-2012) | v2 (24-07-2012) | v3 (11-09-2012) |
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| Special solutions to a compact equation for deep-water gravity waves |
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Francesco Fedele 1, 2Denys Dutykh 3 |
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| (13/04/2012) |
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| Recently, Dyachenko & Zakharov (2011) have derived a compact form of the well known Zakharov integro-differential equation for the third order Hamiltonian dynamics of a potential flow of an incompressible, infinitely deep fluid with a free surface. Special traveling wave solutions of this compact equation are numerically constructed using the Petviashvili method. Their stability properties are also investigated. Further, unstable traveling waves with wedge-type singularities, viz. peakons, are numerically discovered. To gain insights into the properties of singular traveling waves, we consider the academic case of a perturbed version of the compact equation, for which analytical peakons with exponential shape are derived. Finally, by means of an accurate Fourier-type spectral scheme it is found that smooth solitary waves appear to collide elastically, suggesting the integrability of the Zakharov equation. |
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| 1 : | School of Civil and Environmental Engineering |
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Georgia Institute of Technology (Georgia Tech) |
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| 2 : | School of Electrical and Computer Engineering - Georgia Insitute of Technology (ECE GeorgiaTech) |
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Georgia Institute of Technology |
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| 3 : | Laboratoire de Mathématiques (LAMA) |
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CNRS : UMR5127 – Université de Savoie |
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| Domaine | : | Physique/Mécanique/Mécanique des fluides Sciences de l'ingénieur/Mécanique/Mécanique des fluides Mathématiques/Analyse numérique Mathématiques/Equations aux dérivées partielles Science non linéaire/Formation de Structures et Solitons Science non linéaire/Systèmes Solubles et Intégrables Physique/Physique/Dynamique des Fluides Physique/Physique/Physique Atmosphérique et Océanique Physique/Physique/Physique Numérique |
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| water waves – deep water approximation – Hamiltonian structure – travelling waves – solitons |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00687325, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00687325 | |
| oai:hal.archives-ouvertes.fr:hal-00687325 | |
| Contributeur : Denys Dutykh | |
| Soumis le : Lundi 10 Septembre 2012, 22:53:51 | |
| Dernière modification le : Mardi 11 Septembre 2012, 08:33:06 | |
