Interference effects in soliton scattering by impurities

Abstract

We present a comprehensive study ofthe effects of inhomogeneities on nonlinear excitation dynamics in different one-dimensional soliton-bearing systems. We theoretically analyse soliton scattering by one and two point-like impurities in the framework of the perturbed sine-Gordon, nonlinear Schrödinger and Korteweg equations, and predict that interference effects arise in the form of an oscillatory dependence ofthe soliton reflection coefficient on the distance between impurities. The main fanor responsible for this behaviour is the spectral density of the soliton radiation: the values of that distance which are integer multiples of the main wavelength radiated by the soliton upon collision with the inhomogeneities give rise to resonant scattering, with very link reflection. Our approximate analytical predictions explain previous numerical results concerning nonlinear lattices, and are further supported by new simulations that we have performed on.thc sine-Gordon system