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一类反应扩散方程的孤立周期波和局部临界周期分支

古结平 黄文韬 陈挺

古结平, 黄文韬, 陈挺. 一类反应扩散方程的孤立周期波和局部临界周期分支[J]. 应用数学和力学, 2021, 42(2): 221-232. doi: 10.21656/1000-0887.410263
引用本文: 古结平, 黄文韬, 陈挺. 一类反应扩散方程的孤立周期波和局部临界周期分支[J]. 应用数学和力学, 2021, 42(2): 221-232. doi: 10.21656/1000-0887.410263
GU Jieping, HUANG Wentao, CHEN Ting. Solitary Periodic Waves and Local Bifurcations of Critical Periods for a Class of Reaction-Diffusion Equations[J]. Applied Mathematics and Mechanics, 2021, 42(2): 221-232. doi: 10.21656/1000-0887.410263
Citation: GU Jieping, HUANG Wentao, CHEN Ting. Solitary Periodic Waves and Local Bifurcations of Critical Periods for a Class of Reaction-Diffusion Equations[J]. Applied Mathematics and Mechanics, 2021, 42(2): 221-232. doi: 10.21656/1000-0887.410263

一类反应扩散方程的孤立周期波和局部临界周期分支

doi: 10.21656/1000-0887.410263
基金项目: 国家自然科学基金(12061016;12001112);广西自然科学基金(重点项目)(2016GXNSFDA380031);广西研究生教育创新计划项目(YCSW2020105)
详细信息
    作者简介:

    古结平(1996—),男,硕士生(E-mail: gujieping3032@163.com);黄文韬(1966—),男,教授,博士生导师(通讯作者. E-mail: huangwentao@163.com);陈挺(1989—),男,博士(E-mail: chenting0715@126.com).

  • 中图分类号: O175.12

Solitary Periodic Waves and Local Bifurcations of Critical Periods for a Class of Reaction-Diffusion Equations

Funds: The National Natural Science Foundation of China(12061016;12001112)
  • 摘要: 研究了一类含有五次非线性反应项和常数扩散项的反应扩散方程的小振幅孤立周期波解,以及它的行波方程局部临界周期分支问题.运用行波变换将反应扩散方程转换为对应的行波系统,应用奇点量方法和计算机代数软件MATHEMATICA计算出该系统的前8个奇点量,得到该系统奇点的两个中心条件,并证明行波系统原点处可分支出8个极限环,对应的非线性反应扩散方程存在8个小振幅孤立周期波解;通过周期常数的计算,得到了行波系统原点的细中心阶数,并证明该系统最多有3个局部临界周期分支,且能达到3个局部临界周期分支;通过分析行波系统的临界周期分支,得到该反应扩散方程有3个临界周期波长.
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出版历程
  • 收稿日期:  2020-09-07
  • 修回日期:  2020-09-23
  • 刊出日期:  2021-02-01

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