Structural features of steady-state traveling solutions of the Ginzburg–Landau equation in the phase approximation

The article investigated solutions of the Ginzburg–Landau equation in the phase approximation. Families of periodic steady-state traveling solutions branching off from the trivial zero solution were constructed analytically and numerically. The critical values of the parameters at which restructuring of such families takes place have been found. Limitations, beyond which the phase approximation equations widely used in the literature become unacceptable, were indicated. For this model, the structural relationship of periodic solutions with soliton ones was demonstrated. The numerical and analytical results were compared.