Numerical simulations of periodic travelling waves to a generalized Ginzburg-Landau equation

In this paper, we consider a generalized Ginzburg-Landau equation, which describes various pattern formation and the onset of instabilities in nonequilibrium fluid dynamical systems, as well as in the theory of phase transitions and superconductivity. By the means of the Hopf bifurcation theorem, we obtain the constant-amplitude, small-amplitude and variable-amplitude periodic travelling wave solutions to the generalized Ginzburg-Landau equation. Finally we give some numerical simulations.