TRAVELING FRONTS OF A REAL SUPERCRITICAL QUINTIC GINZBURG-LANDAU EQUATION COUPLED BY A SLOW DIFFUSION MODE

Qun Bin; Wentao Huang; Jing Li; Shi Liang

doi:10.11948/20230457

2024 Volume 14 Issue 5

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Qun Bin, Wentao Huang, Jing Li, Shi Liang. TRAVELING FRONTS OF A REAL SUPERCRITICAL QUINTIC GINZBURG-LANDAU EQUATION COUPLED BY A SLOW DIFFUSION MODE[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2862-2876. doi: 10.11948/20230457

Citation:

Qun Bin, Wentao Huang, Jing Li, Shi Liang. TRAVELING FRONTS OF A REAL SUPERCRITICAL QUINTIC GINZBURG-LANDAU EQUATION COUPLED BY A SLOW DIFFUSION MODE[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2862-2876. doi: 10.11948/20230457

TRAVELING FRONTS OF A REAL SUPERCRITICAL QUINTIC GINZBURG-LANDAU EQUATION COUPLED BY A SLOW DIFFUSION MODE

1.
School of Mathematics and Statistics, Guangxi Normal Unversity, Guilin 541006, Guangxi, China
2.
Basic Teaching Department, Guilin University of Electronic Technology, Beihai 536000, Guangxi, China
3.
College of General Education, Guangxi Vocational and Technical College of Water Resources and Electric Power, Nanning 530000, Guangxi, China

Author Bio: Email: binqun1108@163.com(Q. Bin); Email: 2597942474@qq.com(J. Li); Email: 1501288941@qq.com(S. Liang)
Corresponding author: Email: huangwentao@163.com(W. Huang)
Fund Project: The authors were supported by National Natural Science Foundation of China (12061016)

Abstract

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.
- Quintic Ginzburg-Landau equation /
- traveling front solution /
- heteroclinic solution /
- geometric singular perturbation theory /
- Melnikov function
MSC: 35Q56, 35C07, 37G15

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References

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