Tensor Invariants of the Poisson Brackets of Hydrodynamic Type |
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Authors: | Oleg I Bogoyavlenskij |
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Institution: | (1) Department of Mathematics, Queen’s University, Kingston, K7L 3N6, Canada |
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Abstract: | Form-invariant solutions for the Poisson brackets of hydrodynamic type on a manifold M
n
with (2,0)-tensor g
ij
(u) of rank m ≤ n are derived. Tensor invariants of the Poisson brackets are introduced that include a vector field V (or dynamical system V) on M
n
, the Lie derivative L
V
g
ij
and symmetric (k, 0)-tensors . Several scalar invariants of the Poisson brackets are defined. A nilpotent Lie algebra structure is disclosed in the space
of 1-forms that annihilate the (2,0)-tensor g
ij
(u). Applications to the one-dimensional gas dynamics are presented. |
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Keywords: | |
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