华东师范大学学报(自然科学版) ›› 2003, Vol. 2003 ›› Issue (1): 31-37.

• 论文 • 上一篇    下一篇

非线性微分方程一类精确解的计算机自动推导

柳银萍；李志斌   

  1. 华东师范大学 计算机科学技术系，上海 200062
  • 收稿日期:2001-02-15 修回日期:2002-09-04 出版日期:2003-03-25 发布日期:2003-03-25

An Automated Calculating for A Class of Exact Solutions to Nonlinear Differential Equations

LIU Ying-ping; LI Zhi-bin   

  1. Department of Computer Science, East China Normal University, Shanghai 200062, China
  • Received:2001-02-15 Revised:2002-09-04 Online:2003-03-25 Published:2003-03-25

摘要： 以吴文俊数学机械化方法魏基本工具在计算机代数系统Maple 上开发出了非线性演化方程孤波解的自动求解软件包RATH。利用RATH成功求解了近百个不同类型的非线性演化方程，所获结果不仅涵盖了所有的已知解，而且对许多方程还发现了新的解和形式更为一般的解。对于绝大部分方程，RATH 的运行时间都在10秒以内。

关键词: 符号计算, 自动推理, 演化方程, 孤波解, 符号计算, 自动推理, 演化方程, 孤波解

Abstract: By the Mathematics-Mechanization method proposed by Wu Wentsun, a package RATH os developed to output directly the solitary wave solutions to a nonlinear differential equation, based on the maple system. With it nearly one hundred equations have been calculated. The results not only recover all known solutions, but also find some new solutions as well as solutions in the general form. Furthermore, most of the solutions are obtained with the running time no more than 10 seconds under PC Pentium Ⅲ.

Key words: automated reasoning, evolution equation, solitary wave solution, symbolic computation, automated reasoning, evolution equation, solitary wave solution