Hydrodynamic-type systems describing -dimensional polynomially integrable geodesic flows

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• 作者：Gianni Manno^a ; ^{giovanni.manno@polito.it} ; Maxim V. Pavlov^b ; ^c ; ^d ; ^{mpavlov@itp.ac.ru}
• 关键词：53D25 ; 37J35 ; 37K05 ; 37D40 ; 70H05
• 刊名：Journal of Geometry and Physics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：113
• 期：Complete
• 页码：197-205
• 全文大小：434 K
• 卷排序：113

文摘

Starting from a homogeneous polynomial in momenta of arbitrary order we extract multi-component hydrodynamic-type systems which describe 22-dimensional geodesic flows admitting the initial polynomial as integral. All these hydrodynamic-type systems are semi-Hamiltonian, thus implying that they are integrable according to the generalized hodograph method. Moreover, they are integrable in a constructive sense as polynomial first integrals allow to construct generating equations of conservation laws. According to the multiplicity of the roots of the polynomial integral, we separate integrable particular cases.