Topological Soliton Dynamics in Media with Microscopic Rotations

Abstract

Microscopic rotations can play a very important role in the molecular crystals or in some dielectric crystals where atoms are joined in comparatively rigid clusters and the inter-cluster interactions are comparatively weak. The range of unusual phenomena observed in such materials is fascinating, from incommensurate phase to negative Poisson ratio. Here we focus on the topological soliton dynamics in such materials and describe a number of effects, such as the trigger off and propagation of autowaves, soliton multiplication in the metastable media, soliton collisions and annihilations. All these phenomena are addressed in frame of the elastically hinged mo lecule (EHM) model having microscopic particles with rotational degrees of freedom. For this model we construct various continuum approximations. New important features of the continuum models for media with microscopic rotations are the increase in number of equations of motion due to the increase in number of degrees of freedom and the appearance of the higher gradient terms in the resulting equations. We also construct the multi-field continuum approximation capable of description not only long but also short waves.