Transient motion of a solitary wave in elastic ferroelectrics

Abstract

A nonlinear transient wave motion involving the structure in domains and walls occuring in elastic ferroelectric crystals in the neighborhood of their phase transition is presented. Here the transient motion is caused by an applied electric field. Nonlinearly coupled equations governing the translational and rotational motions of the chain in the continuum approximation were obtained on the basis of a crystalline model consisting of an atomic chain equipped with microscopic electric dipoles. In the absence of applied field the equations obtained possess a solitary-wave solution which represents a moving ferroelectric 180° domain wall. Strains and stresses accompagny this solitary wave being generated through electromechanical couplings. When an electric field is present, a perturbation scheme is developed in order to obtain the characteristic parameters of the evolving wave. The method based on the averaged-Lagrangian of Whitham where the parameters depend only on time (adiabatic perturbation), allows one to deduce the velocity and position (or phase) of the ferroelectric solitary wave. By way of conclusion, numerical illustrations are given for the transient motion from rest of the electromechanical solitary wave.