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使用解析方法获得FitzHugh-Nagumo方程新的peakon解

邹丽 王振 梁辉 宗智 邹昊

邹丽, 王振, 梁辉, 宗智, 邹昊. 使用解析方法获得FitzHugh-Nagumo方程新的peakon解[J]. 应用数学和力学, 2013, 34(11): 1141-1149. doi: 10.3879/j.issn.1000-0887.2013.11.003
引用本文: 邹丽, 王振, 梁辉, 宗智, 邹昊. 使用解析方法获得FitzHugh-Nagumo方程新的peakon解[J]. 应用数学和力学, 2013, 34(11): 1141-1149. doi: 10.3879/j.issn.1000-0887.2013.11.003
ZOU Li, WANG Zhen, LIANG Hui, ZONG Zhi, ZOU Hao. Finding New Types of Peakon Solutions for FitzHugh-Nagumo Equation by an Analytical Technique[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1141-1149. doi: 10.3879/j.issn.1000-0887.2013.11.003
Citation: ZOU Li, WANG Zhen, LIANG Hui, ZONG Zhi, ZOU Hao. Finding New Types of Peakon Solutions for FitzHugh-Nagumo Equation by an Analytical Technique[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1141-1149. doi: 10.3879/j.issn.1000-0887.2013.11.003

使用解析方法获得FitzHugh-Nagumo方程新的peakon解

doi: 10.3879/j.issn.1000-0887.2013.11.003
基金项目: 国家重点基础研究发展计划(973计划)资助项目(2010CB832704;2013CB036101); 国家自然科学基金资助项目(51109031;11072053;51009022;51221961;51239002);中国教育部博士点基金资助项目(20100041120037);中央高校基本科研业务费专项资金资助项目(DUTBJS01;DUT12LK52;DUT12LK34)
详细信息
    作者简介:

    邹丽(1981—),女,辽宁盘锦人,副教授,博士,硕士生导师(通讯作者. Tel: +86-411-84706521; E-mail: lizou@dlut.edu.cn).

  • 中图分类号: O242.1;O302

Finding New Types of Peakon Solutions for FitzHugh-Nagumo Equation by an Analytical Technique

Funds: The National Basic Research Program of China (973 Program)(2010CB832704; 2013CB036101);The National Natural Science Foundation of China(51109031; 11072053; 51009022; 51221961; 51239002)
  • 摘要: 依据对FitzHugh-Nagumo方程的研究,通过微分变化法近似分析出FitzHugh-Nagumo方程,获得了这个方程的尖峰孤立波(peakon soliton)的解,从而获得了更多形式的peakon解,同时也分析了微分变换法(differential transform method, DTM)收敛区域和收敛速度.构建的微分变换法,结合帕德(Padé)逼近,构建一个明确的,完全解析,对FitzHugh-Nagumo方程全部有意义的尖波解.其主要思想是限制边界条件而令导数在孤立波不存在峰值,但导数的孤立波在两侧存在.结果表明,微分变换法在参数很小的情况下可以避免摄动的限制.表明这种方法提供了一种强大而有效地获得FitzHugh-Nagumo方程新的peakon解的数学方法.
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出版历程
  • 收稿日期:  2013-06-14
  • 修回日期:  2013-08-19
  • 刊出日期:  2013-11-15

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