Soliton Scattering by an Impurity on a Nonlinear Lattice

Abstract

It has been widely recognized that the study of a propagation of nonlinear waves in disordered media is the key to understanding the interplay between structural disorder and nonlinearity in many physical contexts¹. Is is well known that each leads to Anderson localization due to disorder and soliton due to nonlinearity. Then the problems are; Does a soliton behave as a particle even in the presence of disorder? Does nonlinearity prevent the formation of the localization of modes? These are the theoretical as well as experimental concerns in the field of condensed matter physics. In recent years there have been some theoretical works in these fields. These are mainly concerned with a study of nonlinear localized modes at an impurity site on a discrete lattice^{2, 3} or the soliton scattering by an impurity on continuous one-dimensional model systems⁴. For the problem of a soliton propagation in a model one-dimensional disordered nonlinear lattice there is an attempt to examine the existence of a stationary self-localized nonlinear mode and also a soliton-like mode satisfying a local dispersion relation in the disordered lattice system⁵.