Solitons and electroacoustic interactions in ferroelectric crystals. II. Interactions of solitons and radiations

Multiple-soliton solutions representative of the motion and interaction of walls in ferroelectric crystals of the same type as ${\mathrm{NaNO}}_2$ are studied, both analytically and numerically, on the basis of a set of coupled nonlinear electroacoustic equations deduced in paper I [Phys. Rev. B 30, 5036 (1984)] of the present series. Electromechanical couplings are duly taken into account and, in fact, are responsible for the nonlinear coupling between a d’Alembert wave equation for the transverse elastic displacement and a sine-Gordon equation that governs the orientation of the dipole-carrying molecular group in each lattice cell. To solve this rather complex problem, a singular perturbation technique associated with the methods used for solving nonlinear wave equations (Baaumlcklund transformations, etc.) is developed at the first order in the coupling parameter. This allows one to exhibit the first-order corrective radiative terms which superimpose on the nonlinear zeroth-order solution (multiple soliton), the free parameters of which are modulated in order to satisfy the secularity condition at the first order. Simultaneously, a numerical solution using a Lax-Wendroff finite-difference scheme is obtained which illustrates the analytical considerations and models the soliton-antisoliton collision, the soliton-soliton collision, the ‘‘oscillatory soliton,’’ and the one-soliton solution (already exhibited in paper I on the basis of a double sine-Gordon equation) along with the accompanying elastic displacement field and the radiative contributions.