| 一个简单的变换,双曲函数法和一类反应扩散方程的精确解 |
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| 引用本文： | 于发军.一个简单的变换,双曲函数法和一类反应扩散方程的精确解[J].渤海大学学报(自然科学版),2005,26(3):240-243. |
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| 作者姓名： | 于发军 |
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| 作者单位： | 渤海大学,数学系,辽宁,锦州,121013 |
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| 基金项目： | 辽宁省教育厅资助项目(2021401157) |
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| 摘 要： | 提出一种双曲函数的方法，并且证明了这种变换方法可以从sinh—Gordon方程中得到。用这种方法和关消元法，得到一类反应扩散方程的许多显式和精确行波解。这些解包括孤波解，奇性孤波解，周期解和有理函数解。作为反应扩散方程的特例，也得到Chaffee—Infante和Huxley方程的对应的解。在求解的过程中数学符号计算Mathematiea是一种基本的工具。
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| 关 键 词： | 双曲函数法 多显式和精确行波解 奇性孤波解 |
| 文章编号： | 1673-0569(2005)03-0240-04 |
| 修稿时间： | 2004年7月15日 |
A simple transformation,hyperbolic function method and exact solution for a class of reaction diffusion equation |
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| YU Fa-Jun.A simple transformation,hyperbolic function method and exact solution for a class of reaction diffusion equation[J].Journal of Bohai University:Natural Science Edition,2005,26(3):240-243. |
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| Authors: | YU Fa-Jun |
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| Abstract: | A transformation method which is called hyperbolic function method is proposed.We show that this transformation can be obtained from the sinh-Gordon equation.Using this method and Wu elimination method,many new explicit and exact travelling wave solution are obtained to a class of reaction diffusion equation.These solutions include singular solitary wave solutions,periodic solutions and rational function solution.As a sprcial cases of reaction diffusion equation,Chaffee-Infante equation and Huxley equation also obtain corresponding solutions.Symbolic computation Mathematica is also basic tool during the course of solving problem. |
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| Keywords: | hyperbolic function method explicit and exact travelling wave solution singular solitary wave solution |
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