Large time asymptotic behaviour of solutions of the complex Landau–Ginzburg equation

The asymptotic behaviour for large time of solutions of the Cauchy problem for the complex Landau–Ginzburg equation is described. The initial data are assumed to be small in the multidimensional case (relative to the space variables), and they can be arbitrary in the one-dimensional case. In both cases the leading term is explicitly presented and an estimate for the remainder in the uniform metric is given.