2023/12/04 by Francisco Correa, Correa, Francisco, Octavio Quintana +1
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2312.02013
openalex publication_date 2023/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate new integrable extensions of two-center Coulomb systems. We study the most general n-dimensional deformation of the two-center problem by adding arbitrary functions supporting second order commuting conserved quantities. The system is superintegrable for n>4 and, for certain choices of the arbitrary functions, reduces to known models previously discovered. Then, based on this extended system, we introduce an additional integrable generalisation involving Calogero interactions for n=3. In all examples, including the two-center problem, we explicitly present the complete list of Liouville integrals in terms of second-order integrals of motion.