V. B. Matveev, A. O. Smirnov, “Multiphase solutions of nonlocal symmetric reductions of equations of the AKNS hierarchy: General analysis and simplest examples”, TMF, 2020, Volume 204, Number 3,Pages <nobr>383

This article is cited in 13 papers

Multiphase solutions of nonlocal symmetric reductions of equations of the AKNS hierarchy: General analysis and simplest examples

V. B. Matveev^ab, A. O. Smirnov^c

^a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
^b Institut de Mathématiques de Bourgogne, Université de Bourgogne — Franche Comté, Dijon, France
^c St. Petersburg State University of Aerospace Instrumentation, St. Petersburg, Russia

Abstract: We consider nonlocal symmetries that all or all even (all odd) equations of the AKNS hierarchy have. We construct examples of solutions simultaneously satisfying several nonlocal equations of the AKNS hierarchy. We present a detailed study of single-phase solutions.

Keywords: $\mathcal{PT}$ symmetry, nonlocal model, AKNS hierarchy, nonlinear Schrödinger equation, modified Korteweg–de Vries equation.

Received: 09.03.2020
Revised: 11.04.2020

DOI: 10.4213/tmf9901