2007/06/30 by Artur Sergyeyev, Maciej Błaszak, Maciej Blaszak · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1088/1751-8113/41/10/105205
published as J.Phys.A41:105205,2008 · 21 pages, LaTeX 2e, no figures; major revision; Propositions 2 and 7 and several new references added
arxiv created 2007/12/20 · openalex publication_date 2008/02/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We present a multiparameter generalization of the Stäckel transform (the latter is also known as the coupling-constant metamorphosis) and show that under certain conditions this generalized Stäckel transform preserves Liouville integrability, noncommutative integrability and superintegrability. The corresponding transformation for the equations of motion proves to be nothing but a reciprocal transformation of a special form, and we investigate the properties of this reciprocal transformation. Finally, we show that the Hamiltonians of the systems possessing separation curves of apparently very different form can be related through a suitably chosen generalized Stäckel transform.