The eleventh Peregrine breather and twenty parameters families of solutions to the NLS equation

Abstract : The Peregrine breather of order eleven (P11 breather) solution to the focusing one dimensional nonlinear Schrödinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given : when all parameters are equal to 0 we recover the famous P11 breather. We obtain new families of quasi-rational solutions to the NLS equation in terms of explicit quotients of polynomials of degree 132 in x and t by a product of an exponential depending on t. We study these solutions by giving patterns of their modulus in the (x; t) plane, in function of the different parameters.
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Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01224526
Contributeur : Pierre Gaillard <>
Soumis le : samedi 12 décembre 2015 - 11:10:53
Dernière modification le : mercredi 28 septembre 2016 - 15:47:15
Document(s) archivé(s) le : dimanche 13 mars 2016 - 10:22:19

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hal nlsN11P20TCV6.pdf
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  • HAL Id : hal-01224526, version 2

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Pierre Gaillard, Mickael Gastineau. The eleventh Peregrine breather and twenty parameters families of solutions to the NLS equation. 2015. <hal-01224526v2>

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