Stability analysis for the quartic Landau-Ginzburg model

The three-dimensional stability of static one-dimensional solutions of the Landau-Ginzburg equation is investigated. A general formula for the growth or decay rate is obtained for arbitrary local free energies, using a method developed earlier by Rowlands and Infeld (1979) for different equations. The results are then applied to quartic free energies. Among the real finite solutions obtained earlier, conoidal waves are shown to be stable, and solitary waves and kinks marginally stable. Two other types of non-linear periodic waves are shown to be unstable.