The Neumann–Moser dynamical system and the Korteweg–de Vries hierarchy

Abstract. At the focus of the paper are applications of the well-known Moser transformation of the C. Neumann dynamical system. It yields a new quadratic integrable dynamical system on ( \mathbb{C}^{3n+1} ), which we call the Neumann–Moser dynamical system. We present an explicit formula for the inverse of the Moser transformation. Consequently, we obtain an explicit invertible transformation sending the Uhlenbeck–Devaney integrals of the Neumann system to the integrals of our system. One of the main results is a recurrence for 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.

Recommended citation: Polina Baron. (2024). "The Neumann–Moser dynamical system and the Korteweg–de Vries hierarchy." arXiv:2402.18079.
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