广义Fitzhugh-Nagumo方程的无穷序列新解  

NEW INFINITE SEQUENCE SOLUTIONS OF THE GENERALIZED FITZHUGH-NAGUMO EQUATION

作　　者：伊丽娜[1] 包俊东[1] 套格图桑[1] 

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《动力学与控制学报》2016年第5期385-390,共6页Journal of Dynamics and Control

基　　金：国家自然科学基金(11361040);内蒙古自治区自然科学基金(2015MS0128);内蒙古自治区高等学校科学研究基金(NJZY16180);内蒙古自治区2016年硕士研究生科研创新项目(S20161013502);内蒙古师范大学研究生科研创新基金项目(CXJJS16081)资助的课题~~

摘　　要：利用辅助方程的几种结论,构造了广义Fitzhugh-Nagumo方程的多种无穷序列新解.步骤一,利用函数变换与首次积分,给出了辅助方程的新解、Bcklund变换和解的非线性叠加公式.步骤二,通过函数变换,将广义Fitzhugh-Nagumo方程的求解问题转化为非线性常微分方程的求解问题.步骤三,利用符号计算系统Mathematica与辅助方程的几种结论,构造了广义Fitzhugh-Nagumo方程的多种无穷序列新解.According to several conclusions of auxiliary equation, the new infinite sequence solutions of the gen- eralized Fitzhugh-Nagumo equation is constructed in this paper. Firstly, the function transformation and the first integral are presented to obtain the new solutions, Backlund transformation and the nonlinear solution superposi- tion formula of the auxiliary equation. Secondly, through lutions of the generalized Fitzhugh-Nagumo equation is c the function transformation, the problem to gain the so- hanged to the problem of obtaining the solutions of the nonlinear ordinary differential equations. Thirdly, some conclusions of the auxiliary equation are employed to construct various new infinite sequence solutions of the generalized Fitzhugh-Nagumo equation with the help of symbolic computation system ＇ Mathematica＇.

关 键 词：广义Fitzhugh-Nagumo方程 辅助方程 首次积分 无穷序列新解 

分 类 号：O175[理学—数学]