STABILITY ANALYSIS OF THE DISCRETE LANDAU-GINSBURG EQUATION

The stability of time-independent solutions of a class of discrete nonlinear equations is investigated by extending a method developed earlier to study the stability of the static solutions of the continuous Landau-Ginsburg equation. A simple necessary condition for stability is found and it is shown that all nonlinear wave solutions are unstable while soliton and kink solutions may be stable. A further method is introduced which shows that the soliton solution is in fact unstable whilst the kink is marginally stable.