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Differential Geometry of Hydrodynamic Vlasov Equations | | John Gibbons
; Andrea Raimondo
; | | Date: |
11 Dec 2006 | | Subject: | Exactly Solvable and Integrable Systems | | Abstract: | We consider hydrodynamic chains in $(1+1)$ dimensions which are Hamiltonian with respect to the Kupershmidt-Manin Poisson bracket. These systems can be derived from single $(2+1)$ equations, here called hydrodynamic Vlasov equations, under the map $A^n =int_{-infty}^infty p^n f dp.$ For these equations an analogue of the Dubrovin-Novikov Hamiltonian structure is constructed. The Vlasov formalism allows us to describe objects like the Haantjes tensor for such a chain in a much more compact and computable way. We prove that the necessary conditions found by Ferapontov and Marshall in (arXiv:nlin.SI/0505013) for the integrability of these hydrodynamic chains are also sufficient. | | Source: | arXiv, nlin/0612022 | | Services: | Forum | Review | PDF | Favorites | |
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