Accéder directement au contenu Accéder directement à la navigation
Article dans une revue

Two-Phase Periodic Solutions to the AKNS Hierarchy Equations

Abstract : In this paper, we investigate genus 2 algebro-geometric solutions of the AKNS hierarchy equations strictly periodic with respect to the space variable x. In general, genus 2 solutions, which are expressed in terms of two-dimensional Riemann theta functions, are not strictly periodic in x. We show that x-periodic solutions can be obtained by an appropriate choice of a hyperelliptic spectral curve having a structure of a covering of an elliptic curve. For odd-numbered members of the AKNS hierarchy, these solutions can be made periodic also with respect to the corresponding time variables of the AKNS hierarchy, by imposing further restrictions on the structure of the spectral curve. The corresponding solutions are especially interesting from the point of view of potential applications to the study of signal propagation in nonlinear optical fibers.
Type de document :
Article dans une revue
Liste complète des métadonnées

https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02469321
Contributeur : Imb - Université de Bourgogne <>
Soumis le : jeudi 6 février 2020 - 14:58:36
Dernière modification le : mardi 10 novembre 2020 - 17:14:04

Identifiants

Collections

Citation

Vladimir Matveev, A. Smirnov. Two-Phase Periodic Solutions to the AKNS Hierarchy Equations. Journal of Mathematical Sciences, Springer Verlag (Germany), 2019, 242 (5), pp.722-741. ⟨10.1007/s10958-019-04510-8⟩. ⟨hal-02469321⟩

Partager

Métriques

Consultations de la notice

71