Novikov equations for commuting differential operators of orders 3,4,5

TL;DR

This paper studies Novikov equations related to commuting differential operators of orders 3, 4, and 5, providing explicit Hamiltonian forms and a separation of variables on a genus 2 hyperelliptic curve.

Contribution

It introduces explicit Hamiltonian forms for Novikov equations and demonstrates separation of variables using compatible Poisson brackets.

Findings

Explicit Hamiltonian forms for Novikov equations of orders 3, 4, 5

Separation of variables on a genus 2 hyperelliptic curve

Application of compatible Poisson brackets method

Abstract

We consider Novikov equations for commutative ring generated by differential operators of orders 3,4,5. We present an explicit Hamiltonian form of these equations. Using the method of compatible Poisson brackets, we find a separation of variables on a hyperelliptic curve of genus 2 for the Novikov equations.