| Volume 14, Number 5, 2024, Pages - DOI：10.11948/JAAC-2023-0457 |
| Traveling fronts of a real supercritical quintic Ginzburg-Landau equation coupled by a slow diffusion mode |
| Qun Bin,Wentao Huang,Jing Li,Shi Liang |
| Keywords:Quintic Ginzburg-Landau equation Traveling front solution Heteroclinic solution Geometric singular perturbation theory Melnikov function. |
| Abstract: |
| In this paper, we investigate the existence of traveling front solutions for a class of quintic Ginzburg-Landau equations coupled with a slow diffusion mode. By employing the theory of geometric singular perturbations, we turn the problem into a geometric perturbation problem. We demonstrate the intersection property of the critical manifold and further validate the existence of heteroclinic orbits by computing the zeros of the Melnikov function on the critical manifold. The results demonstrate that under certain parameters, there is 1 or 2 heteroclinic solutions, confirming the existence of traveling front solutions for the considered quintic Ginzburg-Landau equation coupled with a slow diffusion mode. |
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