Bi-Hamiltonian ordinary differential equations with matrix variables

被引：11

作者：

Odesskii, A. V. ^{[1
]}

Rubtsov, V. N. ^{[2
,3
]}

Sokolov, V. V. ^{[4
]}

机构：

[1] Brock Univ, St Catharines, ON L2S 3A1, Canada

[2] Univ Angers, CNRS, LAREMA, Angers, France

[3] Inst Theoret & Expt Phys, Moscow 117259, Russia

[4] RAS, LD Landau Theoret Phys Inst, Moscow 117901, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2012年 / 171卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

integrable ordinary differential equation with matrix unknowns; bi-Hamiltonian formalism; Manakov model; ASSOCIATIVE ALGEBRAS;

D O I：

10.1007/s11232-012-0043-4

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider a special class of Poisson brackets related to systems of ordinary differential equations with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets, and find the corresponding hierarchy of integrable models, which generalizes the two-component Manakov matrix system to the case of an arbitrary number of matrices.

引用

页码：442 / 447

页数：6

共 12 条

[1] On the associative analog of Lie bialgebras [J].