After critical and precritical bifurcations of progressive wave in a generalized Ginzburg–Landau equation

A generalized time dependent Ginzburg–Landau equation is considered with periodic boundary conditions. There is contable number progressive wave. Local bifurcations of that solutions is edudied when they change the stability. The torus of the $2$ dimension bifurcate of each of the progressive wave. In particular, the possibility of precritic hard bifurcation is demonstrated for this equations.