用Riccati方程的新解求Fitzhugh-Nagumo方程的新行波解  

SOLVING NEW TRAVELLING WAVE SOLUTIONS OF THE FITZHUGH-NAGUMO EQUATION USING NEW SOLUTIONS OF THE RICCATI EQUATION

作　　者：林府标 班晓倩 LIN Fu-biao;BAN Xiao-qian(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China)

机构地区：[1]贵州财经大学数统学院,贵州贵阳550025

出　　处：《数学杂志》2022年第2期162-168,共7页Journal of Mathematics

基　　金：贵州省科技计划基金项目(黔科合基础[2019]1051);贵州省教育厅青年科技人才成长项目(黔教合KY字[2017]150);2018年度贵州财经大学校级科研基金项目资助(2018XYB04);贵州财经大学创新探索及学术新苗项目(黔科合平台人才[2017]5736-020);2021年度贵州财经大学校级项目(2021KYYB01)。

摘　　要：本文研究了Riccati方程和Fitzhugh-Nagumo方程的新精确解的构造.利用试探函数法找到了Riccati方程的八种类型的新显式精确解.用广义Tanh函数法结合Riccati方程的新精确解,获得了Fitzhugh-Nagumo方程、Huxley方程、广义KPP方程及Newell-Whitehead方程的许多新显式行波解.最后,广义Tanh函数法结合Riccati方程的新精确解,可用于探寻其它偏微分方程的新行波解.In this paper,we study the construction of new exact solutions for Riccati equation and Fitzhugh Nagumo equation.Eight types explicit and exact solutions of the Riccati equation were found by using the trial function method.Many new explicit travelling wave solutions of the Fitzhugh-Nagumo equation,Huxley equation,extended KPP equation,and Newell-Whitehead equation were obtained by use of the extended Tanh-function method and exact solutions of the Riccati equation.Finally,the extended Tanh-function method and exact solutions to the Riccati equation can be also applied to find new travelling wave solutions of other nonlinear partial differential equations.

关 键 词：RICCATI方程 FITZHUGH-NAGUMO方程 广义Tanh函数法 行波解 

分 类 号：O175.29[理学—数学] O175.14[理学—基础数学]