Lotka-Volterra systems as Poisson-Lie dynamics on solvable groups

被引：0

作者：

Ballesteros, A. ^{[1
]}

Blasco, A. ^{[1
]}

Musso, F. ^{[1
]}

机构：

[1] Univ Burgos, Dept Fis, Burgos 09001, Spain

来源：

XX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS | 2012年 / 1460卷

关键词：

Lotka-Volterra; perturbations; integrable systems; Lie groups; Poisson coalgebras; Casimir functions; N-dimensional; quantum deformations; HAMILTONIAN-STRUCTURE; 1ST INTEGRALS; 3; DIMENSIONS; EQUATIONS; INTEGRABILITY; POLYNOMIALS; INVARIANTS;

D O I：

10.1063/1.4733365

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A class of integrable 3D Lotka-Volterra (LV) equations is shown to be a particular instance of Poisson-Lie dynamics on a family of solvable 3D Lie groups. As a consequence, the classification of all possible Poisson-Lie structures on these groups is shown to provide a systematic approach to obtain multiparametric integrable deformations of this LV system. Moreover, by making use of the coproduct map induced by the group multiplication, a twisted set of 3N-dimensional integrable Lotka-Volterra equations can be constructed. Finally, the quantization of one of the Poisson-Lie LV structures is performed, and is shown to give rise to a quantum euclidean algebra.

引用

页码：115 / 119

页数：5

共 25 条

[1]

[Anonymous], 1956, ELEMENTS MATH BIOL, DOI DOI 10.2307/1909476

[2] (Super)integrability from coalgebra symmetry: formalism and applications [J].