Integrable systems associated with generalized Sklyanin algebra

TL;DR

This paper introduces new integrable systems derived from the Elliptic Schlesinger system using point fusion, featuring higher pole orders and generalized Sklyanin algebra structures.

Contribution

It presents a novel method to generate integrable systems with higher pole orders and quadratic Poisson algebras extending Sklyanin algebras.

Findings

New integrable systems with higher pole orders identified

Quadratic Poisson algebras generalizing Sklyanin algebras constructed

Phase space structures with graduated algebraic properties developed

Abstract

Using the point fusion procedure we obtain the new integrable systems from the Elliptic Schlesinger system (ESS). These new systems have the pole orders higher than one in the matrix of the Lax operator. Quadratic Poisson algebras on the phase space of the new systems generalize the Sklyanin algebras and have the graduated structure.