Soliton dynamics in a microstructured lattice model

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Abstract
The nonlinear dynamics of localized structures of the soliton type in a lattice model involving internal degrees of freedom in rotation is presented. The physical model consists basically of a one-dimensional monoatomic chain equipped with microscopic electric dipoles associated with molecular groups. The model is particularly suitable for molecular ferroelectric crystals such as sodium nitrite exhibiting structures in ferroelectric domains and walls or for long chains of polymers such as crystalline polyethylene or polyvinylidine fluoride and others where molecular groups perform rotational motions. Two main types of motion can be distinguished in this picture: (i) the longitudinal and transverse displacements of the mass centre of the molecular group and (ii) two rigid-body rotational motions of the electric dipoles about the chain axis and perpendicular to it. The propagation of coupled solitons is investigated for two elementary configurations. A situation for which all the dipoles rotate perpendicularly to the chain axis is first studied. A second configuration is next considered when the dipole rotation takes place about the chain axis.