Abstract
Ginzburg–Landau equation plays a very important role in a wide range of physical contexts. Much attention had been given to explore the dynamics of the waves in Ginzburg–Landau equations as well as its various coupled reaction–diffusion systems. In this article, dynamical system techniques such as the methods of geometric singular perturbation theory and Melnikov function are combined to show the persistence (existence) and bifurcations of traveling fronts in a real supercritical Ginzburg–Landau equation coupled by a slow diffusion mode. It is shown that heteroclinic saddle-node bifurcation occurs under certain parametric values such that 1, 2 and even 3 heteroclinic solutions may exist. The critical manifolds of the parameters corresponding to the heteroclinic saddle-node bifurcations are explicitly determined.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
