2004/12/21 by Maxim Pavlov, Pavlov, Maxim
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0412054
to appear in Theoretical and Mathematical Physics
arxiv created 2004/12/21 · arxiv updated 2009/12/01
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).