Soliton-Complex Dynamics in Strongly Dispersive Medium

Abstract

The concept of soliton complex in a nonlinear dispersive medium is proposed. It is shown that strongly interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon is considered to be universal and applicable to various physical systems. The soliton complex and its "excited" states are described analytically and numerically as solutions of nonlinear dispersive equations with the fourth and higher spatial or mixed derivatives. The dispersive sine-Gordon, double and triple sine-Gordon, and piecewise-linear models are studied in detail. Mechanisms and conditions of the formation of soliton complexes, and peculiarities of their stationary dynamics are investigated. A phenomenological approach to the description of the complexes and the classification of all the possible complex states are proposed. Some examples of physical systems, where the phenomenon can be experimentally observed, are briefly discussed.