Nonlocal nonlinear Schrödinger equation and its discrete version: soliton solutions and gauge equivalence (Q2820928)

Searching for solutions of the soliton equations and discovering the relations between different nonlinear evolution equations are important work of studying soliton equations. Many systematic methods have been developed to obtain explicit solutions of soliton equations, among which the Darboux transformation is the most famous one. In this paper, the authors first discussed gauge equivalence of the nonlocal focusing/defocusing NLS equation and their discrete cases. Then, depending on the Darboux transformation, soliton solutions of the discrete nonlocal NLS equations (including the focusing and defocusing cases). As an application, some interesting figures are plotted. The research of the nonlocal NLS equation and the discrete case in this paper has discovered many new properties of these equations.