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

• Autorzy: Misha Bialy , Andrey Mironov
• 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.

Słowa kluczowe

EN

Integral of motion; Magnetic geodesic flows; Riemann invariants; Systems of hydrodynamic type

Kategorie tematyczne

• 70H06: Completely integrable systems and methods of integration
• 35L65: Conservation laws
• 35L67: Shocks and singularities

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 5
• Strony: 1596-1604

Daty

wydano

2012-10-01

online

2012-07-24

Twórcy

autor

Misha Bialy

• Tel Aviv University

autor

Andrey Mironov

• Moscow State University

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
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Identyfikatory

DOI

10.2478/s11533-012-0045-3