Integrable Lotka-Volterra systems

被引：26

作者：

Bogoyavlenskij, O. I. ^{[1
,2
]}

机构：

[1] Queens Univ, Dept Math, Kingston, ON K7L 3N6, Canada

[2] Russian Acad Sci, VA Steklov Math Inst, Moscow 119991, Russia

来源：

REGULAR & CHAOTIC DYNAMICS | 2008年 / 13卷 / 06期

关键词：

Lax representation; Hamiltonian structures; Casimir functions; Riemannian surfaces; Lotka-Volterra systems; integrable lattices;

D O I：

10.1134/S1560354708060051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Infinite- and finite-dimensional lattices of Lotka-Volterra type are derived that possess Lax representations and have large families of first integrals. The obtained systems are Hamiltonian and contain perturbations of Volterra lattice. Examples of Liouville-integrable 4-dimensional Hamiltonian Lotka-Volterra systems are presented. Several 5-dimensional Lotka- Volterra systems are found that have Lax representations and are Liouville-integrable on constant levels of Casimir functions.

引用

页码：543 / 556

页数：14

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