|
| 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. |
| 关键词: Riccati方程 Fitzhugh-Nagumo方程 广义Tanh函数法 行波解 |
| DOI： |
| 分类号:O175.29;O175.14 |
| 基金项目: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). |
|
| SOLVING NEW TRAVELLING WAVE SOLUTIONS OF THE FITZHUGH-NAGUMO EQUATION USING NEW SOLUTIONS OF THE RICCATI EQUATION |
|
LIN Fu-biao,BAN Xiao-qian
|
| Abstract: |
| 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 flnd new travelling wave solutions of other nonlinear partial differential equations. |
| Key words: Riccati equation Fitzhugh-Nagumo equation extended Tanh-function method travelling wave solution |
