Tenth order solutions to the NLS equation with eighteen parameters

Abstract : We present here new solutions of the focusing one dimensional non linear Schrödinger equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain explicit quotients of polynomial of degree 110 in x and t by a product of an exponential depending on t. We construct new patterns of different types of rogue waves and recover the triangular configurations as well as rings and concentric as found for the lower orders.
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Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01165324
Contributeur : Pierre Gaillard <>
Soumis le : jeudi 18 juin 2015 - 18:35:30
Dernière modification le : mercredi 28 septembre 2016 - 15:35:44
Document(s) archivé(s) le : mardi 15 septembre 2015 - 19:21:19

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  • HAL Id : hal-01165324, version 1

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Pierre Gaillard, Mickael Gastineau. Tenth order solutions to the NLS equation with eighteen parameters. 2015. <hal-01165324>

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