2N+1 highest amplitude of the modulus of the N-th order AP breather and other 2N-2 parameters solutions to the NLS equation

Abstract : We construct here new deformations of the AP breather (Akhmediev-Peregrine breather) of order N (or AP N breather) with 2N −2 real parameters. Other families of quasi-rational solutions of the NLS equation are obtained. We evaluate the highest amplitude of the modulus of AP breather of order N ; we give the proof that the highest amplitude of the AP N breather is equal to 2N + 1. We get new formulas for the solutions of the NLS equation, different from these already given in previous works. New solutions for the order 8 and their deformations according to the parameters are explicitly given. We get the triangular configurations as well as isolated rings at the same time. Moreover, the appearance for certain values of the parameters, of new configurations of concentric rings are underscored.
Type de document :
Pré-publication, Document de travail
2015
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-01131608
Contributeur : Pierre Gaillard <>
Soumis le : samedi 14 mars 2015 - 10:54:03
Dernière modification le : mardi 12 janvier 2016 - 12:57:58
Document(s) archivé(s) le : lundi 15 juin 2015 - 10:10:35

Fichier

halnls2NP8GAJPAV7.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01131608, version 1

Collections

Citation

Pierre Gaillard. 2N+1 highest amplitude of the modulus of the N-th order AP breather and other 2N-2 parameters solutions to the NLS equation. 2015. <hal-01131608>

Partager

Métriques

Consultations de
la notice

123

Téléchargements du document

82