S. Kovalevskaya system, its generalization and discretization

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.

15 pages

References in corpus (1)

• On integrability of Hirota-Kimura type discretizations

Cited by in corpus (4)

• Integrability properties of Kahan's method
• Discretization of polynomial vector fields by polarization
• Liouville integrability and superintegrability of a generalized Lotka-Volterra system and its Kahan discretization
• New classes of quadratic vector fields admitting integral-preserving Kahan-Hirota-Kimura discretizations