Nonlinear waves in repulsive media supported by spatially localized parity-time-symmetric potentials

Abstract

We study the existence, stability and dynamics of solitons in a PT-symmetric potential in the presence of a local defocusing nonlinearity. For the sake of concreteness, we refer to Bose–Einstein condensates, where defocusing nonlinearity stems from a repulsive inter-particle interaction. Two kinds of transverse profiles for the gain-loss mechanism, i.e., the imaginary part of the potential, are considered. Differently from the attractive inter-particle interaction, solitons exist only inside a narrow band of chemical potential and particle number. The existence region shrinks as the magnitude of the gain-loss is increased, with the soliton ceasing to exist above the linear exceptional point, that is, the point at which PT symmetry is broken. Using linear stability analysis together with full numerical simulations of the Gross–Pitaevskii equation, we show that solitons survive on temporal scales much longer than the diffusion time. For magnitude of gain-loss close to the exceptional point, stability depends on the transverse profile of the gain-loss mechanism and the magnitude of the nonlinear excitation.