Open AccessOne-phase elliptic solutions of the nonlocal nonlinear equations from AKNS hierarchy and their spectral curves
Author(s) -
А. О. Смирнов,
Е. Э. Аман
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1515/3/032080
Subject(s) - integrable system , hierarchy , mathematics , nonlinear system , phase (matter) , construct (python library) , mathematical analysis , pure mathematics , physics , computer science , quantum mechanics , market economy , programming language , economics
After publishing the pioneering works of Ablowitz and Musslimani, other authors also began active research on nonlocal forms of classical integrable nonlinear equations. They usually investigate particular equations, and for these equations they construct solutions that are expressed in terms of elementary functions. In present paper, we investigate one-phase elliptic solutions of all the equations from the AKNS hierarchy, including mixed ones. We also analyze the properties of spectral curves of the considered one-phase solutions in order to be able to construct multiphase algebro-geometric solutions of nonlocal forms of the AKNS hierarchy equations in the future.