Kowalevski top revisited

TL;DR

This paper revisits the Kowalevski top, exploring its separation of variables, generalization to algebra o(4), and introduces a new Lax matrix using quadratic r-matrix formalism, revealing its interpretation as a B2 integrable lattice.

Contribution

It provides a new Lax matrix for the Kowalevski top and links its separation equations to integrable lattice structures, enhancing understanding of its integrability.

Findings

New 2x2 Lax matrix constructed

Separation equations linked to B2 integrable lattice

Generalization to algebra o(4) analyzed

Abstract

We review the separation of variables for the Kowalevski top and for its generalization to the algebra o(4). We notice that the corresponding separation equations allow an interpretation of the Kowalevski top as a B2 integrable lattice. Consequently, we apply the quadratic r-matrix formalism to construct a new 2x2 Lax matrix for the top, which is responsible for its separation of variables.