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Description of compatible differential-geometric Poisson brackets of the first order

Maxim Pavlov
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Abstract

Compatible local differential-geometric Poisson brackets of the first order (Dubrovin-Novikov type) are classified by solutions of modified Sinh-Gordon equation. It was proved by E.V. Ferapontov. In this paper integrable system describing compatible non-local differential-geometric Poisson brackets of the first order (Ferapontov type) is presented in case when one metric is flat and another one has co-dimension 1. This is a reduction of the Cherednik model (chiral fields).

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Maxim Pavlov. 2004-12-21. Description of compatible differential-geometric Poisson brackets of the first order. https://arxiv.org/abs/nlin/0412054

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