Nonlinear waves in para-and ferroelectrics described by the Landau-Khalatnikov equation

The propagation of an extremely short (one cycle long) pulse of an electromagnetic field in a medium with two equilibrium states is considered theoretically. The analysis is based on the set of Maxwell equations and the Landau-Khalatnikov equation, in which the approximations of the slowly varying envelopes are not used. The solutions of this set that describe the steady-state propagation of a solitary polarization wave and of an electromagnetic pulse are found. In the approximation of a unidirectional wave, a numerical simulation of the propagation and interaction of solitary waves is performed in terms of the model considered.