Fitzhugh-Nagumo方程行波解及孤立波解  

Multiple Traveling Wave Solutions and Solitary Wave Solutions for Fitzhugh-Nagumo Equation

作　　者：陈自高[1] 张金辉[1] 

机构地区：[1]华北水利水电学院数学与信息科学学院,河南郑州450011

出　　处：《河南工程学院学报（自然科学版）》2010年第4期57-60,共4页Journal of Henan University of Engineering：Natural Science Edition

基　　金：河南省教育厅自然科学基金(2010A110012)

摘　　要：提出了寻找非线性发展方程显式精确解的新的辅助方程法,作为实例通过选取变系数Bernoulli方程作为辅助常微分方程,借助于它并根据齐次平衡原则,求解了Fitzhugh-Nagumo方程,并得到了该方程新的显式精确解,其中包括一般形式的行波解、扭状正则孤立波解和奇异孤立波解,此方法可以应用到其他类似方程的求解上去.A new auxiliary equation method for seeking explicit exact solutions for nonlinear evolution equations is proposed.As an example the variable-coefficient Bernoulli equation is chosen as auxiliary ordinary differential equation,with the help of which and according to homogeneous balance principle,some new explicit exact solutions for the Fitzhugh-Nagumo equation,which include traveling wave solutions,kink regular solitary wave solutions and singular solitary wave solutions are obtained.The method used here could be applied to solve other similar equations.

关 键 词：变系数辅助方程法 FITZHUGH-NAGUMO方程 行波解 孤立波解 

分 类 号：O175.2[理学—数学]