Integrable deformations of Lotka-Volterra systems

Details Integrable deformations of Lotka-Volterra systems Integrable deformations of Lotka-Volterra systems

2011-06-04

arxiv.org/abs/1106.0805v2

Physics Letters A 375 (2011) 3370-3374

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, revised version. The paper has been shortened and some comments and references have been added

Scientific paper

10.1016/j.physleta.2011.07.055

The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited from a novel point of view by showing that the quadratic Poisson structure underlying its integrability structure is just a real three-dimensional Poisson-Lie group. As a consequence, the Poisson coalgebra map that is given by the group multiplication provides the keystone for the explicit construction of a new family of 3N-dimensional integrable systems that, under certain constraints, contain N sets of deformed versions of the 3D LV equations. Moreover, by considering the most generic Poisson-Lie structure on this group, a new two-parametric integrable perturbation of the 3D LV system through polynomial and rational perturbation terms is explicitly found.

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