STABILITY ANALYSIS FOR THE QUARTIC LANDAU-GINZBURG MODEL .2

A previous investigation of the stability of static one-dimensional solutions of the Landau-Ginzburg equation with a quartic non-linearity is extended. Exact spatially varying solutions are modified by small amplitude, time-dependent perturbations. In contradiction to the case of part I of this study, these are not assumed to have small frequency omega and small decay rates gamma. We show that all periodic solutions, as well as the solitary waves, are unstable with respect to this new type of perturbations. The kink solution is stable with respect to all perturbations considered. When the results of both parts of this paper are put together, we obtain an extensive stability analysis of static solutions to the Landau-Ginzburg equation. This equation is important in fluid dynamics, solid state and superconductivity theory, as well as other branches of physics. The paper is self-contained and can be read independently of part I.