Lie symmetries and their local determinacy for a class of differential-difference equations

被引：25
|
作者：
Jiang, ZH [1 ]
机构：
[1] Univ New England, Dept Math Stat & Comp Sci, Armidale, NSW 2351, Australia
来源：
PHYSICS LETTERS A | 1998年 / 240卷 / 03期
关键词：
differential-difference equations; Lie point symmetries; integrability;
D O I：
10.1016/S0375-9601(98)00099-1
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Differential-difference equations (DDEs) u(n)((k))(t) = F-n(t, u(n+a),..., u(n+b)) for k greater than or equal to 2 are studied for their differential Lie symmetries. We observe that while nonintrinsic Lie symmetries do exist in such DDEs, a great many admit only the intrinsic ones. We also propose a mechanism for automating symmetry calculations for fairly general DDEs, with a variety of features exemplified. In particular, the Fermi-Pasta-Ulam system is studied in detail and its new similarity solutions given explicitly. (C) 1998 Published by Elsevier Science B.V.
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页码：137 / 143
页数：7
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