耦合慢扩散模式的五次实Ginzburg-Landau方程的脉冲解存在性

doi:10.13438/j.cnki.jdzk.2024.04.002

吉首大学学报（自然科学版） ›› 2024, Vol. 45 ›› Issue (4): 5-10.DOI: 10.13438/j.cnki.jdzk.2024.04.002

耦合慢扩散模式的五次实Ginzburg-Landau方程的脉冲解存在性

宾群，欧阳宇婷，杜超雄

（1.广西师范大学数学与统计学院，广西桂林 541006；2.长沙师范学院数学科学学院，湖南长沙 410000）

出版日期:2024-07-25 发布日期:2024-07-23
作者简介:宾群（1996—），女，广西玉林人，广西师范大学数学与统计学院在读研究生，主要从事微分方程理论与应用研究.
基金资助:
国家自然科学基金资助项目（12061016）；湖南省教育厅重点项目（22A719）

Existence of Pulse Solutions for the Quintic Real Ginzburg-Landau Equation with Coupled Slow Diffusion Mode

BIN Qun,OUYANG Yuting,DU Chaoxiong

（1.Department of Mathematics and Statistics,Guangxi Normal University,Guilin 541006,Guangxi China;2.School of Mathematics and Science,Changsha Normal University,Changsha 410000,China)

Online:2024-07-25 Published:2024-07-23

摘要/Abstract

摘要：利用Fenichel的几何奇异摄动理论，将一个耦合慢扩散模式的次临界五次实Ginzburg-Landau方程脉冲解的存在性问题转化为几何摄动问题，展示了临界流形之间的横截相交性，并通过计算临界流形上Melnikov函数的零点进一步验证了同宿轨道的存在性.在一定的参数条件下，证明了慢扩散的次临界五次实Ginzburg-Landau方程有脉冲解.

关键词： 五次实Ginzburg-Landau方程, 脉冲解, 几何摄动, 同宿轨道, Melnikov函数

Abstract: Utilizing Fenichel's geometric singular perturbation theory,we transform the problem of pulse solution existence for a coupled subcritical quintic real Ginzburg-Landau equation with slow diffusion mode into a geometric perturbation scenario,showing the transversality between critical manifolds.Through the computation of the Melnikov function's zeros on the critical manifolds,the presence of homoclinic orbits is further confirmed.Ultimately,it is demonstrated that,under specific parameter conditions,the subcritical quintic Ginzburg-Landau equation with slow diffusion exhibits pulse solutions.

Key words: quintic real Ginzburg-Landau equation, pulse solution, geometric perturbation, homoclinic orbit, Melnikov function

宾群, 欧阳宇婷, 杜超雄. 耦合慢扩散模式的五次实Ginzburg-Landau方程的脉冲解存在性[J]. 吉首大学学报（自然科学版）, 2024, 45(4): 5-10.

BIN Qun, OUYANG Yuting, DU Chaoxiong. Existence of Pulse Solutions for the Quintic Real Ginzburg-Landau Equation with Coupled Slow Diffusion Mode[J]. Journal of Jishou University(Natural Sciences Edition), 2024, 45(4): 5-10.

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耦合慢扩散模式的五次实Ginzburg-Landau方程的脉冲解存在性

Existence of Pulse Solutions for the Quintic Real Ginzburg-Landau Equation with Coupled Slow Diffusion Mode

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