S. Kovalevskaya system, its generalization and discretization

TL;DR

This paper explores the Kovalevskaya system, demonstrating its equivalence to the Euler top, proposing two integrable discretizations, and extending it to a generalized form with discretization analysis.

Contribution

It establishes the isomorphism between the Kovalevskaya system and the Euler top, introduces two new integrable discretizations, and generalizes the system with a focus on discretization methods.

Findings

Proved the Kovalevskaya system is isomorphic to the Euler top.

Developed two integrable discretizations of the system.

Presented a generalized Kovalevskaya system with discretization analysis.

Abstract

We consider an integrable three-dimensional system of ordinary differential equations introduced by S.V. Kovalevskaya in a letter to G. Mittag-Leffler. We prove its isomorphism with the three-dimensional Euler top, and propose two integrable discretizations for it. Then we present an integrable generalization of the Kovalevskaya system, and study the problem of integrable discretization for this generalized system.