On generalized Volterra systems

JOURNAL OF GEOMETRY AND PHYSICS

卷:87

Article

Charalambides, S. A.¹  Damianou, P. A.¹  Evripidou, C. A.¹ 

[1] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

关键词: Lotka-Volterra;    Integrable systems;    Root systems;    KM-system;    Toda lattice;   

DOI  :  10.1016/j.geomphys.2014.07.007

来源: Elsevier

【 摘 要 】

We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The algorithm uses the root system of a complex simple Lie algebra. The Hamiltonian vector field is homogeneous cubic but in a number of cases a simple change of variables transforms such a system to a quadratic Lotka Volterra system. We present in detail all such systems in the cases of A(3), A(4) and we also give some examples from higher dimensions. We classify all possible Lotka Volterra systems that arise via this algorithm in the A(n) case. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free