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

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.

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Publication Details

Journal
ArXiv.org
Published
2025-07-20
Primary Topic
Nonlinear Waves and Solitons
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article
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article

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

G. B. Shabat, В. В. Соколов, A. V. Tsiganov
ArXiv.org
Nonlinear Waves and Solitons
article

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

G. B. Shabat, В. В. Соколов, A. V. Tsiganov
article en

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.

ArXiv.org
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Nonlinear Waves and Solitons
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Novikov equations for commuting differential operators of orders 3,4,5 — G. B. Shabat, В. В. Соколов, et al. · ArXiv.org (2025) | TGRS Research Map | TGRS