Lie point symmetries of differential-difference equations

被引：17

作者：

Levi, D. ^{[1
,2
]}

Winternitz, P. ^{[3
,4
]}

Yamilov, R. I. ^{[5
]}

机构：

[1] Univ Roma Tre, Dipartimento Ingn Elettron, I-00146 Rome, Italy

[2] Sezione Ist Nazl Fis Nucl, I-00146 Rome, Italy

[3] Univ Montreal, Ctr Rech Math, Montreal, PQ H3C 3J7, Canada

[4] Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada

[5] Russian Acad Sci, Ufa Inst Math, Ufa 450008, Russia

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2010年 / 43卷 / 29期

基金：

加拿大自然科学与工程研究理事会; 俄罗斯基础研究基金会;

关键词：

INTEGRABILITY;

D O I：

10.1088/1751-8113/43/29/292002

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present an algorithm for determining the Lie point symmetries of differential equations on fixed non-transforming lattices, i.e. equations involving both continuous and discrete-independent variables. The symmetries of a specific integrable discretization of the Krichever-Novikov equation, the Toda lattice and Toda field theory are presented as examples of the general method.

引用

页数：14

共 28 条

[1] Symmetry approach to the integrability problem [J].

Adler, VÉ ;

Shabat, AB ;

Yamilov, RI .

THEORETICAL AND MATHEMATICAL PHYSICS, 2000, 125 (03) :1603-1661

[2]

[Anonymous], 1983, Sov. Math. Dokl

[3]

[Anonymous], 1979, SOV MATH DOKL

[4] Difference schemes with point symmetries and their numerical tests [J].

Bourlioux, A. ;

Cyr-Gagnon, C. ;

Winternitz, P. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (22) :6877-6896

[5]

DORODNITSYN V, 2001, GROUP PROPERTIES DIF

[6]

DUBROVIN BA, 1985, ITOGI NAUKI TEKHNIKI, P179

[7] INTEGRABLE NON-LINEAR KLEIN-GORDON EQUATIONS AND TODA-LATTICES [J].

FORDY, AP ;

GIBBONS, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1980, 77 (01) :21-30

[8] HOLOMORPHIC BUNDLES OVER ALGEBRAIC-CURVES AND NON-LINEAR EQUATIONS [J].

KRICHEVER, IM ;

NOVIKOV, SP .

RUSSIAN MATHEMATICAL SURVEYS, 1980, 35 (06) :53-79

[9] DARBOUX TRANSFORMATIONS FOR HIGHER-RANK KADOMTSEV-PETVIASHVILI AND KRICHEVER-NOVIKOV EQUATIONS [J].

LATHAM, GA ;

PREVIATO, E .

ACTA APPLICANDAE MATHEMATICAE, 1995, 39 (1-3) :405-433

[10] Conditions for the existence of higher symmetries of evolutionary equations on the lattice [J].

Levi, D ;

Yamilov, R .

JOURNAL OF MATHEMATICAL PHYSICS, 1997, 38 (12) :6648-6674

← 1 2 3 →