New Examples of Systems of the Kowalevski Type

TL;DR

This paper introduces new integrable dynamical systems of Kowalevski type, utilizing discriminantly separable polynomials to develop an integration method involving genus two theta-functions, expanding the understanding of such systems.

Contribution

It presents novel examples of integrable systems and a new integration approach based on discriminantly separable polynomials, extending Kowalevski's classical method.

Findings

New integrable systems of Kowalevski type constructed

Integration procedure involving genus two theta-functions developed

Role of discriminantly separable polynomials clarified

Abstract

A new examples of integrable dynamical systems are constructed. An integration procedure leading to genus two theta-functions is presented. It is based on a recent notion of discriminantly separable polynomials. They have appeared in a recent reconsideration of the celebrated Kowalevski top, and their role here is analogue to the situation with the classical Kowalevski integration procedure.