Exact solutions of the (1+1)–dimensional nonlocal nonlinear Schrodinger equation

Abstract

: In this paper we consider the (1+1)–dimensional nonlocal nonlinear Schrоdinger equation. The (1+1)–dimensional
nonlocal nonlinear Schrodinger equation is integrable by the inverse scattering method. We used the Darboux transformation to this equation. In addition, a determinant representation of a one–fold, two–fold, and n–fold Darboux transformation of the (1+1)–dimensional nonlocal nonlinear Schrodinger equation is obtained. Using these results, we can construct other soliton and soliton-like solutions (soliton–like: dynamic and topological soliton, periodic, domain walls, kink, lamp, bright and dark solitons, bright and dark rogue waves, bright and dark positons, etc.) of this equation.