Symmetry reduction for the three-dimensional Landau-Ginzburg equation

Abstract

The three-dimensional time-dependent Landau-Ginzburg equation has been used to describe the kinetics of first and second order spontaneous and field-induced phase transitions with nonconservative order parameters. The method of symmetry reduction has been applied to reduce this PDE to a set of ODEs and the corresponding symmetry variables have been found. These equations and the symmetry variables are discussed and analysed. Explicit forms of some exact solutions are presented.