Deformation of dark solitons in a PT-invariant variable coefficients nonlocal nonlinear Schrödinger equation

We derive dark and antidark soliton solutions of a parity-time reversal (PT)-invariant variable coefficients nonlocal nonlinear Schrödinger (NNLS) equation. We map the considered equation into a defocusing PT-invariant NNLS equation with a constraint between dispersion, nonlinearity, and gain/loss parameters. We show that the considered system is PT-invariant only when the dispersion and nonlinearity coefficients are even functions and gain/loss coefficient is an odd function. The characteristics of the constructed dark soliton solutions are investigated with four different forms of dispersion parameters, namely, (1) constant, (2) periodically distributed, (3) exponentially distributed, and (4) periodically and exponentially distributed dispersion parameter. We analyze in detail how the nonlocal dark soliton profiles get deformed in the plane wave background with these dispersion parameters.