Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach

Vladimir Matveev; Aleksandr Smirnov

Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach

Vladimir Matveev ^{1, 2} Aleksandr Smirnov ²

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

2 SUAI - Saint-Petersburg State University of Aerospace Instrumentation

Abstract : We describe a unified structure of solutions for all equations of the Ablowitz–Kaup–Newell–Segur hierarchy and their combinations. We give examples of solutions that satisfy different equations for different parameter values. In particular, we consider a rank-2 quasirational solution that can be used to investigate many integrable models in nonlinear optics. An advantage of our approach is the possibility to investigate changes in the behavior of a solution resulting from changing the model.

Keywords : Nonlinear Schrödinger equation Freak wave Rogue wave AKNS hierarchy Hirota equation

Type de document :

Article dans une revue

Domaine :

Mathématiques [math]

Physique [physics]

Physique [physics] / Physique mathématique [math-ph]

Liste complète des métadonnées

https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01407785
Contributeur : Imb - Université de Bourgogne <>
Soumis le : vendredi 2 décembre 2016 - 15:18:03
Dernière modification le : vendredi 8 juin 2018 - 14:50:07

Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach

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Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach

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