2024/02/28 by Baron, Polina
#35Q53 #37J35 #37K10 (Primary) #37N05 #70H06 (Secondary) #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2402.18079
At the focus of the paper are applications of the well-known Moser transformation of the C. Neumann dynamical system. It yields us a new quadratic integrable dynamical system on ℂ3n+1, which we call the Neumann-Moser dynamical system. We present an explicit formula of the inverse of the Moser transformation. Consequently, we obtain explicitly an invertible transformation of the Uhlenbeck-Devaney integrals of the Neumann system into the integrals of our system. One of the main results of the paper is the recurrent solutions of the Neumann-Moser system. We show that every solution of our system solves the Mumford dynamical system, and vice versa. Every solution of the Neumann-Moser system is proven to solve the stationary Korteweg-de Vries hierarchy. As a corollary, we construct explicit solutions of the Neumann-Moser system in hyperelliptic Kleinian functions.