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Soliton propagation dynamics under the presence of a complex potential areinvestigated. A large variety of qualitatively different potentials, includingperiodic, semi-infinite periodic and localized potentials, is considered. Casesof both symmetric and non-symmetric potentials are studied in terms of theireffect on soliton dynamics. The rich set of dynamical features of solitonpropagation include dynamical trapping, periodic and non-periodic soliton massvariation and non-reciprocal scattering dynamics. These features aresystematically investigated with the utilization of an effective particle phasespace approach which is shown in remarkable agreement with direct numericalsimulations. The generality of the results enables the consideration ofpotential applications where the inhomogeneity of the gain and loss isappropriately engineered in order to provide desirable soliton dynamics.

Soliton dynamics in symmetric and non-symmetric complex potentials