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| HAL : hal-00650528, version 3 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (11-12-2011) | v2 (15-09-2012) | v3 (16-09-2012) |
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| Degenerate determinant representation of solutions of the NLS equation, higher Peregrine breathers and multi-rogue waves. |
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| Pierre Gaillard 1 |
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| (10/12/2011) |
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| We present a new representation of solutions of the focusing NLS equation as a quotient of two determinants. This work is based on a recent paper in which we have constructed a multi-parametric family of this equation in terms of wronskians. This formulation was written in terms of a limit involving a parameter. Here we give a very compact formulation without presence of a limit. This is a completely new result which gives a very efficient procedure to construct families of quasi-rational solutions of the NLS equation. With this method, we construct Peregrine breathers of orders N=4 to 7 and multi-rogue waves associated by deformation of parameters. |
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| 1 : | Institut de Mathématiques de Bourgogne (IMB) |
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CNRS : UMR5584 – Université de Bourgogne |
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| Domaine | : | Mathématiques/Physique mathématique |
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| Riemann theta functions – fredholm determinants – Wronskians – NLS equation – Peregrine breathers – Akhmediev's breathers – Rogue waves |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00650528, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00650528 | |
| oai:hal.archives-ouvertes.fr:hal-00650528 | |
| Contributeur : Pierre Gaillard | |
| Soumis le : Dimanche 16 Septembre 2012, 11:23:13 | |
| Dernière modification le : Dimanche 16 Septembre 2012, 15:20:17 | |
