| Nagumo方程行波系统的定性分析及其有界行波解 |
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| 引用本文： | 李向正,张卫国,原三领.Nagumo方程行波系统的定性分析及其有界行波解[J].应用数学,2011,24(2). |
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| 作者姓名： | 李向正 张卫国 原三领 |
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| 作者单位： | 1. 上海理工大学理学院,上海200093;河南科技大学数学与统计学院,河南洛阳471003
2. 上海理工大学理学院,上海,200093 |
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| 基金项目： | 国家自然科学基金资助项目(10871129); 上海市重点学科建设计划(S30501); 上海市自然科学基金项目(10ZR1420800); 河南科技大学科研创新能力培育基金项目(2010CZ0016) |
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| 摘 要： | 本文对Nagumo方程的行波系统进行了定性分析,该系统存在一端连接鞍点的有界异宿轨,进而选择奇点为鞍点的平面线性自治系统,利用该平面自治系统轨线向径的斜率,根据齐次平衡原则,构造出了Nagumo方程行波系统的行波解.其次Nagumo方程的行波系统还存在着对应中心周围闭轨的周期解,因而提出新的CPP解法,求出了对应的周期解.
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| 关 键 词： | Nagumo方程 行波解 定性分析 LS解法 CPP解法 |
Qualitative Analysis of Traveling Wave System of Nagumo Equation and its Bounded Traveling Wave Solutions |
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| LI Xiangzheng
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ZHANG Weiguo
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YUAN Sanling.Qualitative Analysis of Traveling Wave System of Nagumo Equation and its Bounded Traveling Wave Solutions[J].Mathematica Applicata,2011,24(2). |
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| Authors: | LI Xiangzheng ZHANG Weiguo YUAN Sanling |
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| Institution: | LI Xiangzheng1,2,ZHANG Weiguo1,YUAN Sanling1 (1.College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China,2.College of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471003,China) |
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| Abstract: | The qualitative analysis on Nagumo equation's traveling system has been carried through in this paper.There is a bounded heteroclinic orbit whose one end connects with a saddle point for the traveling wave system.Then a linear plane autonomous system whose singular point is a saddle point is chosen,by means of the system orbit vector's slope,and according to homogeneous balance principle,the traveling wave solutions of Nagumo equation's traveling system are constructed.Second,there are also periodic solutio... |
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| Keywords: | Nagumo equation Traveling wave solution Qualitative analysis LS method CPP method |
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