کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1896972 | 1044472 | 2007 | 14 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Differential geometry of hydrodynamic Vlasov equations Differential geometry of hydrodynamic Vlasov equations](/preview/png/1896972.png)
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 An=∫−∞∞pnfdp. 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 [E.V. Ferapontov, D.G. Marshall, Differential–geometric approach to the integrability of hydrodynamic chains: The Haantjes tensor. arXiv:nlin.SI/0505013, 2005] for the integrability of these hydrodynamic chains are also sufficient.
Journal: Journal of Geometry and Physics - Volume 57, Issue 9, August 2007, Pages 1815–1828