Compatible Poisson brackets on Lie algebras

被引：44

作者：

Bolsinov, AV ^{[1
]}

Borisov, AV ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow 119899, Russia

来源：

MATHEMATICAL NOTES | 2002年 / 72卷 / 1-2期

基金：

俄罗斯基础研究基金会;

关键词：

compatible Poisson brackets; compatible Hamiltonian representation; Lax representation; integrable Hamiltonian system; bi-Hamiltonian vector field; Lie algebra;

D O I：

10.1023/A:1019856702638

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss the relationship between the representation of an integrable system as an L-A-pair with a spectral parameter and the existence of two compatible Hamiltonian representations of this system. We consider examples of compatible Poisson brackets on Lie algebras, as well as the corresponding integrable Hamiltonian systems and Lax representations.

引用

页码：10 / 30

页数：21

共 31 条

[11] ABOUT THE EXISTENCE OF RECURSION OPERATORS FOR COMPLETELY INTEGRABLE HAMILTONIAN-SYSTEMS NEAR A LIOUVILLE TORUS
BROUZET, R
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1993, 34 (04) : 1309 - 1313
[12] Gel'fand I., 1979, FUNCT ANAL APPL, V13, P13, DOI 10.1007/BF01078363
[13] Gelfand I.M., 1993, GELF MATH SEM 1990 1, P51
[14] WEBS, VERONESE CURVES, AND BIHAMILTONIAN SYSTEMS
GELFAND, IM
ZAKHAREVICH, I
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 99 (01) : 150 - 178
[15] KOTTER F, 1900, SITZUNGSBER KONIGL P, V6, P79
[16] SIMPLE-MODEL OF INTEGRABLE HAMILTONIAN EQUATION
MAGRI, F
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1978, 19 (05) : 1156 - 1162
[17] Manakov SV., 1976, Funct. Anal. Appl, V10, P93, DOI [DOI 10.1007/BF01076037, 10.1007/BF01076037]
[18] MESHCHERYAKOV MV, 1983, USP MAT NAUK, V38, P201
[19] Mishchenko A. S., 1978, IZV AKAD NAUK SSSR S, V42, P386
[20] MISHCHENKO AS, 1979, P SEM VECT TENS AN 1, P3

← 1 2 3 4 →