Dynamical behaviour of solitons in a 𝒫𝒯-invariant nonlocal nonlinear Schrödinger equation with distributed coefficients

Abstract

We present one-, two- and three-soliton solutions of a parity-time (𝒫𝒯)-invariant nonlocal nonlinear Schrodinger (NNLS) equation with distributed coefficients, namely dispersion, nonlinearity and loss/gain parameters. We map the considered equation into constant coefficient 𝒫𝒯-invariant NNLS equation with a constraint. We prove that the considered system is 𝒫𝒯-invariant only when the distributed coefficients are even functions. To investigate the dynamical behaviour of the constructed one- and two-soliton solutions, we consider three different forms of dispersion parameters, namely (i) constant, (ii) periodically distributed, and (iii) exponentially distributed one. We report how the intensity profiles of solitons get modified in the background by considering the aforementioned dispersion parameters. By performing asymptotic analysis, we also explain how the dispersion parameters influence the interactions of nonlocal solitons.