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Compatible Poisson brackets of hydrodynamic type

E. V. Ferapontov
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Abstract

Some general properties of compatible Poisson brackets of hydrodynamic type are discussed, in particular: (1) an invariant differential-geometric criterion of the compatibility based on the Nijenhuis tensor; (2) the Lax pair with a spectral parameter governing compatible Poisson brackets in the diagonalizable case; (3) the connection of this problem with the class of surfaces in Euclidean space which possess nontrivial deformations preserving the Weingarten operator.

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E. V. Ferapontov. 2000-05-23. Compatible Poisson brackets of hydrodynamic type. https://doi.org/10.1088/0305-4470%2F34%2F11%2F328

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