Nagumo方程行波系统的定性分析及其有界行波解  

Qualitative Analysis of Traveling Wave System of Nagumo Equation and its Bounded Traveling Wave Solutions

作　　者：李向正[1,2] 张卫国[1] 原三领[1] 

机构地区：[1]上海理工大学理学院,上海200093 [2]河南科技大学数学与统计学院,河南洛阳471003

出　　处：《应用数学》2011年第2期290-295,共6页Mathematica Applicata

基　　金：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)

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.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 solutions of traveling wave system of Nagumo equation corresponding the closed orbits near the center,and then we propose a new method called CPP method,by which the period solutions of the system are obtained.

关 键 词：Nagumo方程 行波解 定性分析 LS解法 CPP解法 

分 类 号：O175.2[理学—数学]