General soliton solutions to a $$\varvec{(2+1)}$$ ( 2 + 1 ) -dimensional nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions

Abstract

We investigate a $$(2+1)$$ -dimensional nonlocal nonlinear Schrodinger equation with the self-induced parity-time symmetric potential. By employing the Hirota’s bilinear method and the KP hierarchy reduction method, general soliton solutions to the $$(2+1)$$ -dimensional nonlocal NLS equation with zero and nonzero boundary conditions are derived. These solutions are given in forms of Gram-type determinants. We first construct general bright solitons with zero boundary condition by constraining the tau functions of two-component KP hierarchy. Furthermore, we derive general dark and antidark solitons with nonzero boundary from the tau functions of single-component KP hierarchy.