Interference effects in soliton scattering by impurities

Abstract

The authors present a comprehensive study of the effects of inhomogeneities on nonlinear excitation dynamics in different one-dimensional soliton-bearing systems. They theoretically analyse soliton scattering by one and two point-like impurities in the framework of the perturbed sine-Gordon, nonlinear Schrodinger and Korteweg-de Vries equations, and predict that interference effects arise in the form of an oscillatory dependence of the soliton reflection coefficient on the distance between impurities. The main factor 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 little reflection. Their approximate analytical predictions explain previous numerical results concerning nonlinear lattices, and are further supported by new simulations that they have performed on the sine-Gordon system. Show more