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.
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页码：543 / 556
页数：14
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