Systems of the Kowalevski type and discriminantly separable polynomials

TL;DR

This paper introduces a class of integrable dynamical systems derived from discriminantly separable polynomials, enabling explicit solutions in genus two theta-functions, akin to the classical Kowalevski top analysis.

Contribution

It constructs new integrable systems based on discriminantly separable polynomials, extending classical methods to a broader class of dynamical systems.

Findings

Explicit integration in genus two theta-functions

Includes examples like Sokolov systems and Jurdjevic elasticae

Generalizes Kowalevski's approach to new systems

Abstract

Starting from the notion of discriminantly separable polynomials of degree two in each of three variables, we construct a class of integrable dynamical systems. These systems can be integrated explicitly in genus two theta-functions in a procedure which is similar to the classical one for the Kowalevski top. The discriminnatly separable polynomials play the role of the Kowalevski fundamental equation. The natural examples include the Sokolov systems and the Jurdjevic elasticae.