1999/10/18 by A. Ballesteros, Ángel Ballesteros, Ballesteros, A. +2
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #nlin.SI #solv-int
paper · pdf · doi:10.48550/arxiv.solv-int/9910009
14 pages Latex
arxiv created 1999/10/18 · openalex publication_date 1999/10/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two dimensional classical integrable systems and different integrable deformations for them are derived from phase space realizations of classical sl(2) Poisson coalgebras and their q-deformed analogues. Generalizations of Morse, oscillator and centrifugal potentials are obtained. The N=2 Calogero system is shown to be sl(2) coalgebra invariant and the well-known Jordan-Schwinger realization can be also derived from a (non-coassociative) coproduct on sl(2). The Gaudin Hamiltonian associated to such Jordan-Schwinger construction is presented. Through these examples, it can be clearly appreciated how the coalgebra symmetry of a hamiltonian system allows a straightforward construction of different integrable deformations for it.