| 非线性微分差分方程守恒律的计算机自动推导 |
| |
| 引用本文： | 朱娇锋,柳银萍.非线性微分差分方程守恒律的计算机自动推导[J].华东师范大学学报(自然科学版),2010,2010(1):24-33. |
| |
| 作者姓名： | 朱娇锋 柳银萍 |
| |
| 作者单位： | 华东师范大学计算机科学技术系,上海,200241 |
| |
| 基金项目： | 国家自然科学基金项目 |
| |
| 摘 要： | 基于吴消元法和"分治"策略,改进了基于标度不变性构造非线性微分差分方程多项式形式守恒律的待定系数算法,并在计算机代数系统Maple上实现了改进后的算法,其中的软件包CLawDDEs可自动推导出微分差分方程的守恒密度及连带流.对于参数化的微分差分方程,CLawDDEs还能自动过滤出无穷守恒律存在的相容性条件.因此,CLawDDEs可作为测试非线性微分差分方程是否可积的有效工具.
|
| 关 键 词： | 微分差分方程 守恒律 标度不变性 可积性 符号计算 微分差分方程 守恒律 标度不变性 可积性 符号计算 |
| 收稿时间： | 2009-5-6 |
| 修稿时间： | 2009-6-22 |
Computer automated derivation of conservation laws for nonlinear differential-difference equations |
| |
| ZHU Jiao-feng,LIU Yin-ping.Computer automated derivation of conservation laws for nonlinear differential-difference equations[J].Journal of East China Normal University(Natural Science),2010,2010(1):24-33. |
| |
| Authors: | ZHU Jiao-feng LIU Yin-ping |
| |
| Institution: | Department of Computer Science and Technology, East China Normal University,Shanghai 200241, China |
| |
| Abstract: | Based on Wu's elimination method and "divide-and-conquer" strategy, the undetermined coefficient method for constructing polynomial conservation laws of nonlinear differential-difference equations was improved. Furthermore, a Maple package CLawDDEs was developed to automatically derive conserved densities and associated fluxes of poly-nomial differential-difference equations. For parameterized nonlinear differential-difference equations, CLawDDEs can also filter out the compatibility conditions which admit the existence of infinitely conservation laws. So CLawDDEs can be used as an effective tool to test the integrability of nonlinear differential-difference equations. |
| |
| Keywords: | differential-difference equations conservation laws scaling invariance integrability symbolic computation |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《华东师范大学学报(自然科学版)》浏览原始摘要信息 |
| 点击此处可从《华东师范大学学报(自然科学版)》下载免费的PDF全文 |
