求某些非线性偏微分方程特解的一个简洁方法

刘式适; 付遵涛; 刘式达; 赵强

求某些非线性偏微分方程特解的一个简洁方法

1.
北京大学地球物理系, 北京 100871;
2.
北京大学湍流研究国家重点实验室, 北京 100871

基金项目: 国家自然科学基金重点资助项目(40035010);科技部攀登特别支持费资助

详细信息

作者简介:
刘式适(1938- ),男,江苏扬州人,教授,博士生导师

中图分类号: O175;O411
计量
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- 被引次数: 0
出版历程
- 收稿日期: 2000-05-08
- 修回日期: 2000-11-26
- 刊出日期: 2001-03-15

A Simple Fast Method in Finding Particular Solutions of Some Nonlinear PDE

1.
Department of Geophysics, Peking University, Beijing 100871, P R China;
2.
SKLTR, Peking University, Beijing 100871, P R China

摘要

摘要: 简单介绍了应用一个简洁的“试探函数法”求解非线性偏微分方程的基本步骤,主要研究了两大类方程,一类是Burgers方程或KdV方程的推广,另一类是具有特殊非线性反应率的Fisher方程.不难看出,这个方法是简洁的,并且可望进一步扩展.
- 试探函数法 /
- 非线性偏微分方程 /
- 冲击波解 /
- 孤立波解
Abstract: The "trial function method"(TFM for short) and a routine way in finding traveling wave solutions to some nonlinear partial differential equations(PDE for short) wer explained.Two types of evolution equations are studied,one is a generalized Burgers or KdV equation,the other is the Fisher equation with special nonlinear forms of its reaction rate term.One can see that this method is simple,fast and allowing further extension.
- trial function method /
- nonlinear PDE /
- shock wave solution /
- solitary wave solution

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参考文献(13)

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