Soliton dynamics in symmetric and non-symmetric complex potentials

Soliton propagation dynamics under the presence of a complex potential are investigated. A large variety of qualitatively different potentials, including periodic, semi-infinite periodic and localized potentials, is considered. Cases of both symmetric and non-symmetric potentials are studied in terms of their effect on soliton dynamics. The rich set of dynamical features of soliton propagation includes dynamical trapping, periodic and non-periodic soliton mass variation and non-reciprocal scattering 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.