Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation

We discuss the existence and non-existence of front, domain wall and pulse type traveling wave solutions of a Ginzburg-Landau equation with cubic terms containing spatial derivatives and a fifth order term, in both subcritical and supercritical cases. Our results appear to be the first rigorous existence and non-existence proofs for the full equation with all possible terms derived from second order perturbation theory present.