Matrix Lax polynomials, geometry of Prym varieties and systems of Hess-Appel'rot type

Abstract

We consider a four-dimensional generalization of Hess-Appel'rot system and costruct its Lax pair. Both classical and algebro-geometric integration procedure are proceeded. The algebro-geometric integration is based on deep facts from geometry of Prym varieties such as the Mumford relation and Mumford-Dalalyan theory. The integration is similar to the integration of Lagrange bitop which has recetly been performed by the authors.