Abstract
We apply the bifurcation theory for planar dynamical systems to the 2D Ginzburg-Landau equation. We construct all the possible traveling wave solutions, some of which are completely new and others have been introduced previously in El Achab and Amine (Nonlinear Dyn 91:995-999, 2018) and Hassan et al. (Eur Phys J Plus 134:425-437, 2019). Furthermore, three-dimensional and two-dimensional graphics of the new solutions are introduced.