On the kinetics of the first order phase transitions

An attempt is made to analyse the kinetics of the first order structural phase transitions on the basis of the Landau-Ginzburg equation. Two simple solutions are proposed: One in the form of one-dimensional solitary wave which can be considered as a planar interface separating two phases and travelling along direction normal to the interface. Any direction of propagation is possible. The other solution has a form of a onedimensional kink-antikink couple which under supercooling conditions reveals properties of a critical nucleus. A short discussion of the free energy density form for one- and multidimensional order parameters, and of the symmetry of the quadratic gradient term is included.