CONTINUOUS SYMMETRIES OF DIFFERENTIAL DIFFERENCE-EQUATIONS - THE KAC-VANMOERBEKE EQUATION AND PAINLEVE REDUCTION

被引：108

作者：

QUISPEL, GRW ^{[1
]}

CAPEL, HW ^{[1
]}

SAHADEVAN, R ^{[1
]}

机构：

[1] UNIV AMSTERDAM, INST THEORET FYS, 1018 XE AMSTERDAM, NETHERLANDS

来源：

PHYSICS LETTERS A | 1992年 / 170卷 / 05期

关键词：

D O I：

10.1016/0375-9601(92)90891-O

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A method is given to derive the point symmetries of partial differential-difference equations. Applying the method to the Kac-van Moerbeke equation we find its symmetries form a Kac-Moody-Virasoro algebra. Using the symmetries, a similarity reduction of the Kac-van Moerbeke equation to an ordinary differential-difference equation is obtained. This reduced equation possesses a Lax pair, reduces to the first Painleve equation in the continuum limit, and satisfies a recently proposed discrete version of the Painleve property.

引用

页码：379 / 383

页数：5

共 31 条

[1]

Ablowitz M. J., 1981, SOLITONS INVERSE SCA

[2] A CONNECTION BETWEEN NON-LINEAR EVOLUTION-EQUATIONS AND ORDINARY DIFFERENTIAL-EQUATIONS OF P-TYPE .1. [J].

ABLOWITZ, MJ ;

RAMANI, A ;

SEGUR, H .

JOURNAL OF MATHEMATICAL PHYSICS, 1980, 21 (04) :715-721

[3]

Bluman G. W., 1989, SYMMETRIES DIFFERENT

[4]

Bluman G.W., 1974, SIMILARITY METHODS D

[5] INTEGRABLE SYMPLECTIC MAPS [J].

BRUSCHI, M ;

RAGNISCO, O ;

SANTINI, PM ;

TU, GZ .

PHYSICA D, 1991, 49 (03) :273-294

[6] COMPLETE-INTEGRABILITY OF LAGRANGIAN MAPPINGS AND LATTICES OF KDV TYPE [J].

CAPEL, HW ;

NIJHOFF, FW ;

PAPAGEORGIOU, VG .

PHYSICS LETTERS A, 1991, 155 (6-7) :377-387

[7] THE DRESSING METHOD, SYMMETRIES, AND INVARIANT SOLUTIONS [J].

FOKAS, AS ;

MANAKOV, SV .

PHYSICS LETTERS A, 1990, 150 (8-9) :369-374

[8] DISCRETE PAINLEVE EQUATIONS AND THEIR APPEARANCE IN QUANTUM-GRAVITY [J].

FOKAS, AS ;

ITS, AR ;

KITAEV, AV .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1991, 142 (02) :313-344

[9] DO INTEGRABLE MAPPINGS HAVE THE PAINLEVE PROPERTY [J].

GRAMMATICOS, B ;

RAMANI, A ;

PAPAGEORGIOU, V .

PHYSICAL REVIEW LETTERS, 1991, 67 (14) :1825-1828

[10]

HILL JM, 1982, PITMAN RES NOTES MAT, V63

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