Unidirectional soliton flows in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric potentials

Abstract

We study the soliton scattering by parity-time- (PT) symmetric potentials and demonstrate that, for a certain range of parameters, both single and multiple soliton scattering exhibit almost perfect unidirectional flow. We employ direct numerical simulations of the corresponding nonlinear Schr\"odinger equation combined with the analysis of the effective equations derived by the collective-coordinate approach and reveal that the physical mechanism behind this effect of the unidirectional scattering is related to the energy exchange between the soliton center of mass and its internal mode.