One-phase elliptic solutions of the nonlocal nonlinear equations from AKNS hierarchy and their spectral curves

Abstract

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.