On general solitons in the parity-time-symmetric defocusing nonlinear Schrödinger equation

Abstract

Via the Hirota bilinear method combined with the Kadomtsev–Petviashvili (KP) hierarchy reduction method, two types of solitons, namely general solitons on a background of periodic waves and rational soliton solutions, to the parity-time-symmetric nonlocal nonlinear Schrodinger equation with the defocusing-type nonlinearity for nonzero boundary condition are investigated. These two types of soliton solutions are constructed by constraining the tau functions of single-component KP hierarchy satisfying the dimension reduction and the nonlocal symmetry and the complex conjugated conditions. For the solitons on a background of periodic waves, we first construct the periodic solution to provide the background of periodic waves and then combine the periodic solution with general soliton solution, which generate solitons on a background of periodic waves. For the rational solitons, we mainly investigate the dynamical behaviours of interactions between several individual rational dark–antidark solitons, antidark–antidark solitons, and antidark–dark solitons, which are elastic collisions with no phase shift. The degenerated soliton cases are also discussed, in which only one-antidark soliton survives.