On the reduction methods for ordinary differential equations

被引：62

作者：

Pucci, E ^{[1
]}

Saccomandi, G

机构：

[1] Univ Studi Perugia, Dipartimento Ingn Ind, I-06125 Perugia, Italy

[2] Univ Lecce, Dipartimento Ingn Innovaz, Sez Ingn Ind, I-73100 Lecce, Italy

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2002年 / 35卷 / 29期

关键词：

D O I：

10.1088/0305-4470/35/29/314

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A standard method based on the use of differential invariants of a Lie group, g, enables us to reduce any ordinary differential equation invariant under the action of g. We show that this method is applicable to vector fields more general than those associated with Lie symmetries. We characterize all such vector fields and study their relationship with nonlocal symmetries and; symmetries.

引用

页码：6145 / 6155

页数：11

共 50 条

[31] ERODE: A Tool for the Evaluation and Reduction of Ordinary Differential Equations
Cardelli, Luca
Tribastone, Mirco
Tschaikowski, Max
Vandin, Andrea
TOOLS AND ALGORITHMS FOR THE CONSTRUCTION AND ANALYSIS OF SYSTEMS, TACAS 2017, PT II, 2017, 10206 : 310 - 328
[32] Reduction of underdetermined systems of ordinary differential equations: II
V. I. Elkin
Differential Equations, 2010, 46 : 1525 - 1536
[33] Reduction of underdetermined systems of ordinary differential equations: IV
V. I. Elkin
Differential Equations, 2012, 48 : 1437 - 1443
[34] Reduction of underdetermined systems of ordinary differential equations: IV
Elkin, V. I.
DIFFERENTIAL EQUATIONS, 2012, 48 (11) : 1437 - 1443
[35] Reduction of underdetermined systems of ordinary differential equations: III
V. I. Elkin
Differential Equations, 2011, 47 : 1556 - 1562
[36] Reduction of Underdetermined Systems of Ordinary Differential Equations: III
Elkin, V. I.
DIFFERENTIAL EQUATIONS, 2011, 47 (11) : 1556 - 1562
[37] Reduction of Linear Hamiltonian Systems of Ordinary Differential Equations
Kireev, I. V.
APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES (AMITANS'15), 2015, 1684
[38] Reduction of underdetermined systems of ordinary differential equations: I
V. I. Elkin
Differential Equations, 2009, 45 : 1721 - 1731
[39] Reduction of underdetermined systems of ordinary differential equations: V
Elkin, V. I.
DIFFERENTIAL EQUATIONS, 2015, 51 (01) : 1 - 10
[40] Reduction of underdetermined systems of ordinary differential equations: I
Elkin, V. I.
DIFFERENTIAL EQUATIONS, 2009, 45 (12) : 1721 - 1731

← 1 2 3 4 5 →