INTERACTION OF A SOLITON WITH POINT IMPURITIES IN AN INHOMOGENEOUS, DISCRETE NONLINEAR SCHRODINGER SYSTEM

We develop a comprehensive perturbation theory for the inhomogeneous, discrete one-dimensional nonlinear Schrodinger equation based on the i nverse scattering transform. We also discuss single-soliton dynamics w ithin the adiabatic approximation and derive higher order corrections to this approximation. Using this perturbation theory, we study in det ail the motion of a soliton interacting with a point impurity, either nondissipative or dissipative, in the presence of a spatially linear p otential. We predict that there are two kinds of dynamical localizatio n of a soliton in the presence of the nondissipative impurity, dependi ng on the impurity strength. One is the usual dynamical localization, which is qualitatively the same as the one in the absence of the impur ity, and the other is the pinning of a soliton by an impurity of suffi cient strength. The predictions of these phenomena and their various d ynamical properties are confirmed by numerical simulations of the full system.