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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 142, Number 2, Pages 293–309
DOI: https://doi.org/10.4213/tmf1783 (Mi tmf1783) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The description of pairs of compatible first-order differential geometric poisson brackets

M. V. Pavlov

Loughborough University
Full-text PDF (252 kB) Citations (1)
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DOI: https://doi.org/10.4213/tmf1783
Abstract: We show that bi-Hamiltonian structures of systems of hydrodynamic type can be described in terms of solutions of nonlinear equations. These equations can be integrated by the inverse scattering transform for arbitrary metrics as well as for flat ones. In particular, if one metric is flat and the other has a constant curvature, then the corresponding integrable system is a reduction of the Cherednik chiral-field model.
Keywords: Hamiltonian structure, Riemann invariant, system of hydrodynamic type.
English version:
Theoretical and Mathematical Physics, 2005, Volume 142, Issue 2, Pages 244–258
DOI: https://doi.org/10.1007/s11232-005-0008-y
Bibliographic databases:
Language: Russian
Citation: M. V. Pavlov, “The description of pairs of compatible first-order differential geometric poisson brackets”, TMF, 142:2 (2005), 293–309; Theoret. and Math. Phys., 142:2 (2005), 244–258
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
\yr 2005
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\pages 244--258
\crossref{https://doi.org/10.1007/s11232-005-0008-y}
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  • https://www.mathnet.ru/eng/tmf1783
  • https://doi.org/10.4213/tmf1783
  • https://www.mathnet.ru/eng/tmf/v142/i2/p293
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:415
    Full-text PDF :240
    References:60
    First page:2
     
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