华东师范大学学报（自然科学版）
華東師範大學學報（自然科學版）
화동사범대학학보（자연과학판）
JOURNAL OF EAST CHINA NORMAL UNIVERSITY(NATURAL SCIENCE)
2010年
1期
24-33
,共10页
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%守恆律%標度不變性%可積性%符號計算
미분차분방정%수항률%표도불변성%가적성%부호계산
differential-difference equations%conservation laws%scaling invaxiance%integrability%symbolic computation
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.
基于吳消元法和"分治"策略,改進瞭基于標度不變性構造非線性微分差分方程多項式形式守恆律的待定繫數算法,併在計算機代數繫統Maple上實現瞭改進後的算法,其中的軟件包CLawDDEs可自動推導齣微分差分方程的守恆密度及連帶流.對于參數化的微分差分方程,CLawDDEs還能自動過濾齣無窮守恆律存在的相容性條件.因此,CLawDDEs可作為測試非線性微分差分方程是否可積的有效工具.
기우오소원법화"분치"책략,개진료기우표도불변성구조비선성미분차분방정다항식형식수항률적대정계수산법,병재계산궤대수계통Maple상실현료개진후적산법,기중적연건포CLawDDEs가자동추도출미분차분방정적수항밀도급련대류.대우삼수화적미분차분방정,CLawDDEs환능자동과려출무궁수항률존재적상용성조건.인차,CLawDDEs가작위측시비선성미분차분방정시부가적적유효공구.
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.
