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2012 | 10 | 5 | 1596-1604
Tytuł artykułu

New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider magnetic geodesic flows on the two-torus. We prove that the question of existence of polynomial in momenta first integrals on one energy level leads to a semi-Hamiltonian system of quasi-linear equations, i.e. in the hyperbolic regions the system has Riemann invariants and can be written in conservation laws form.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
5
Strony
1596-1604
Opis fizyczny
Daty
wydano
2012-10-01
online
2012-07-24
Twórcy
autor
Bibliografia
  • [1] Bialy M., On periodic solutions for a reduction of Benney chain, NoDEA Nonlinear Differential Equations Appl., 2009, 16(6), 731–743 http://dx.doi.org/10.1007/s00030-009-0032-y
  • [2] Bialy M., Integrable geodesic flows on surfaces, Geom. Funct. Anal., 2010, 20(2), 357–367 http://dx.doi.org/10.1007/s00039-010-0069-4
  • [3] Bialy M., Richness or semi-Hamiltonicity of quasi-linear systems which are not in evolution form, preprint available at http://arxiv.org/abs/1101.5897
  • [4] Bialy M., Mironov A.E., Rich quasi-linear system for integrable geodesic flows on 2-torus, Discrete Contin. Dyn. Syst., 2011, 29(1), 81–90 http://dx.doi.org/10.3934/dcds.2011.29.81
  • [5] Bialy M., Mironov A.E., Cubic and quartic integrals for geodesic flow on 2-torus via system of hydrodynamic type, Nonlinearity, 2011, 24(12), 3541–3554 http://dx.doi.org/10.1088/0951-7715/24/12/010
  • [6] Bolotin S.V., First integrals of systems with gyroscopic forces, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1984, 6, 75–82 (in Russian)
  • [7] Dubrovin B.A., Novikov S.P., Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory, Russian Math. Surveys, 1989, 44(6), 35–124 http://dx.doi.org/10.1070/RM1989v044n06ABEH002300
  • [8] Gibbons J., Tsarev S.P., Reductions of the Benney equations, Phys. Lett. A, 1996, 211(1), 19–24 http://dx.doi.org/10.1016/0375-9601(95)00954-X
  • [9] Kozlov V.V., Symmetries, Topology, and Resonances in Hamiltonian Mechanics, Ergeb. Math. Grenzgeb., 31, Springer, Berlin, 1996
  • [10] Mokhov O.I., Ferapontov E.V., Nonlocal Hamiltonian operators of hydrodynamic type that are connected with metrics of constant curvature, Russian Math. Surveys, 1990, 45(3), 218–219 http://dx.doi.org/10.1070/RM1990v045n03ABEH002351
  • [11] Pavlov M.V., Tsarev S.P., Tri-Hamiltonian structures of Egorov systems of hydrodynamic type, Funct. Anal. Appl., 2003, 37(1), 32–45 http://dx.doi.org/10.1023/A:1022971910438
  • [12] Sévennec B., Géométrie des Systèmes Hyperboliques de Lois de Conservation, Mém. Soc. Math. France (N.S.), 56, Société Mathématique de France, Marseille, 1994
  • [13] Ten V.V., Polynomial first integrals of systems with gyroscopic forces, Math. Notes, 2000, 68(1–2), 135–138
  • [14] Tsarev S.P., The geometry of Hamiltonian systems of hydrodynamic type. The generalized hodograph method, Math. USSR-Izv., 1991, 37(2), 397–419 http://dx.doi.org/10.1070/IM1991v037n02ABEH002069
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0045-3
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