Abstract
The degenerate Ginzburg-Landau equation gives a description of patterns which arise in the case of weakly unstable PDEs with a unbounded spatial direction when the Landau constant (characterizing the influence of the nonlinearity) is small. This equation possesses a family of periodic solutions, moreover there exists a band of stable periodic solutions among them. We give the full description of the possible behaviour of the system just outside this stable band. This is done through derivation of the so-called modulated modulation equations. We also study some solutions of these equations among which stationary periodic and heteroclinic solutions, moving solitons, cnoidal waves and front-like solutions are found.
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