Compatible Poisson brackets of hydrodynamic type
Differential Geometry
2009-10-31 v1
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.
Keywords
Cite
@article{arxiv.math/0005221,
title = {Compatible Poisson brackets of hydrodynamic type},
author = {E. V. Ferapontov},
journal= {arXiv preprint arXiv:math/0005221},
year = {2009}
}
Comments
14 pages