Compatible Poisson brackets of hydrodynamic type

Details Compatible Poisson brackets of hydrodynamic type Compatible Poisson brackets of hydrodynamic type

2000-05-23

arxiv.org/abs/math/0005221v1

Mathematics

Differential Geometry

14 pages

Scientific paper

10.1088/0305-4470/34/11/328

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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