Picosecond autowaves near phase transition temperature of the order-disorder type ferroelectrics

In the present work a new phenomenological approach to the accounting for relaxation near the phase transition temperature of the order-disorder type ferroelectric have been proposed. This approach is presented in the framework of pseudospin formalism and is based on the analogies with like those accounting for in para- and ferromagnetics. A relation between phase relaxation time of the critical vibrations, frequency of tunneling oscillations and the average constant of dipole-dipole interactions (or phase transition temperature) is found. This relation was obtained by using of mean field approximation. From differential equations for pseudospin components the Landau - Khalatnikov like equation for macroscopic ferroelectric polarization has been obtained. Self-consistence investigation of the last non-linear equation and Maxwell's equations is carried out in the low-frequency nonresonant regime. It is shown that in paraphase the dynamics of picosecond electromagnetic perturbations yields to the Modified Korteweg - de Vries - Burgers equation. At the same time in ferroelectric phase these perturbations are described by the Korteweg - de Vries - Burgers equation. It is shown that electromagnetic shock wave and autowave formation near phase transition temperature is possible.