The Soliton Concept in Lattice Dynamics

Abstract

In previous chapters we have considered nonlinear waves in the macroworld. We have examined different systems which provide the simplest examples of one-dimensional systems or devices, where the localized waves or pulses called solitons can be simply and coherently created, easily observed, and manipulated on a macroscopic scale. At the microscopic level the localized nonlinear wave modes have a spatial extension ranging from less than a few microns to a few angströms. These excitations, which correspond to large-amplitude atomic or molecular motions, are mainly created by thermal processes, sometimes by some external stimulus; their experimental manifestation is indirect; their observation is more subtle than for the nonlinear macrowaves. This should explain why the number of experimental investigations is rather small compared to the considerable body of literature devoted to theoretical and numerical studies.