Dynamical properties of the classical continuousXYmodel in a time-dependent magnetic field

Abstract

The classical continuous XY model - defined as the two-component normalized spin-field - within a time-dependent magnetic field is investigated. It is shown that the dynamics of the spin-field is governed by the elliptic sine-Gordon equation in which the time dependence is built into the time-dependent external magnetic field. This equation is solved by using the covariant Hamilton-Jacobi equation technique and the Backlund transformation method. The reasons for the poor dynamics of the model are discussed.