Damianou P. Generalized Toda and Volterra systems, talk at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic (abstract)

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Speaker: Pantelis Damianou

Title: Generalized Toda and Volterra systems

Abstract:
We define  some new,  integrable Toda and Volterra type systems. More specifically, we  construct a large family of Hamiltonian systems which interpolate between  the tridiagonal and full version of the system. In the case of Toda there is one such system for every nilpotent ideal  in the  Borel subalgebra. In the case of Volterra lattices, the  Hamiltonian vector field of the new systems is homogeneous cubic but in a number of cases a simple change of variables transforms such a system to a quadratic Lotka-Volterra system.

Slides: Damianou P. Generalized Toda and Volterra systems (presentation at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic).pdf