Soliton dynamics in complex potentials

Abstract

Soliton propagation dynamics under the presence of a complex potential are investigated. Cases of both symmetric and non-symmetric potentials are studied in terms of their effect on soliton dynamics. The existence of an invariant of soliton propagation under specific symmetry conditions for the real and the imaginary part of the potential is shown. The rich set of dynamical features of soliton propagation include dynamical trapping, periodic and nonperiodic soliton mass variation and non-reciprocal dynamics. These features are systematically investigated with the utilization of an effective particle phase space approach which is shown in remarkable agreement with direct numerical simulations. The generality of the results enables the consideration of potential applications where the inhomogeneity of the gain and loss is appropriately engineered in order to provide desirable soliton dynamics.