English

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.

Keywords

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

R2 v1 2026-06-28T14:12:32.199Z