Algebraic curves as a source of separable multi-Hamiltonian systems
Exactly Solvable and Integrable Systems
2024-08-07 v2 Mathematical Physics
math.MP
Abstract
In this paper we systematically consider various ways of generating integrable and separable Hamiltonian systems in canonical and in non-canonical representations from algebraic curves on the plane. In particular, we consider St\"ackel transform between two pairs of St\"ackel systems, generated by 2n-parameter algebraic curves on the plane, as well as Miura maps between St\"ackel systems generated by (n+N)-parameter algebraic curves, leading to multi-Hamiltonian representation of these systems.
Cite
@article{arxiv.2401.04673,
title = {Algebraic curves as a source of separable multi-Hamiltonian systems},
author = {Maciej Blaszak and Krzysztof Marciniak},
journal= {arXiv preprint arXiv:2401.04673},
year = {2024}
}
Comments
Version accepted for publication in Special Issue 2 of Open Communications in Nonlinear Mathematical Physics. One reference added, some language issues fixed, additional explanations in Introduction