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TMF, 1987, Volume 73, Number 2, Pages 316–320 (Mi tmf5634)  

This article is cited in 11 scientific papers (total in 11 papers)

Hamiltonian formalism of weakly nonlinear hydrodynamic systems

M. V. Pavlov


Abstract: Systems of quasilinear equations are considered which are diagonalizable and Hamiltonian, with the condition $\partial_iv^i=0$ where $u_t^i=v^i(u)u_x^i$, $i=1,…,N$. Conservation laws of such systems are found as well as metrics and Poisson brackets. By concrete examples the procedure of finding the solutions is demonstrated. Conditions of the existence of solutions and continuity of commuting flows are pointed out.

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English version:
Theoretical and Mathematical Physics, 1987, 73:2, 1242–1245

Bibliographic databases:

Received: 15.12.1986

Citation: M. V. Pavlov, “Hamiltonian formalism of weakly nonlinear hydrodynamic systems”, TMF, 73:2 (1987), 316–320; Theoret. and Math. Phys., 73:2 (1987), 1242–1245

Citation in format AMSBIB
\Bibitem{Pav87}
\by M.~V.~Pavlov
\paper Hamiltonian formalism of weakly nonlinear hydrodynamic systems
\jour TMF
\yr 1987
\vol 73
\issue 2
\pages 316--320
\mathnet{http://mi.mathnet.ru/tmf5634}
\zmath{https://zbmath.org/?q=an:0653.76005|0632.76001}
\transl
\jour Theoret. and Math. Phys.
\yr 1987
\vol 73
\issue 2
\pages 1242--1245
\crossref{https://doi.org/10.1007/BF01017597}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1987P005000016}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. A. Dubrovin, S. P. Novikov, “Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory”, Russian Math. Surveys, 44:6 (1989), 35–124  mathnet  crossref  mathscinet  zmath  adsnasa
    2. E. V. Ferapontov, “Integration of weekly nonlinear semi-hamiltonian systems of hydrodynamic type by methods of the theory of webs”, Math. USSR-Sb., 71:1 (1992), 65–79  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. R. Kudashev, S. E. Sharapov, “Generalized hodograph method from the group-theoretical point of view”, Theoret. and Math. Phys., 85:2 (1990), 1155–1159  mathnet  crossref  mathscinet  zmath  isi
    4. Ferapontov, EV, “Reciprocal transformations of Hamiltonian operators of hydrodynamic type: Nonlocal Hamiltonian formalism for linearly degenerate systems”, Journal of Mathematical Physics, 44:3 (2003), 1150  crossref  isi
    5. Blaszak, M, “A COORDINATE-FREE CONSTRUCTION OF CONSERVATION LAWS AND RECIPROCAL TRANSFORMATIONS FOR A CLASS OF INTEGRABLE HYDRODYNAMIC-TYPE SYSTEMS”, Reports on Mathematical Physics, 64:1–2 (2009), 341  crossref  isi
    6. El G.A., Kamchatnov A.M., Pavlov M.V., Zykov S.A., “Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions”, J Nonlinear Sci, 21:2 (2011), 151–191  crossref  isi
    7. Lorenzoni P., Pedroni M., “Natural Connections for Semi-Hamiltonian Systems: The Case of the epsilon-System”, Lett Math Phys, 97:1 (2011), 85–108  crossref  isi
    8. M. V. Pavlov, V. B. Taranov, G. A. El, “Generalized hydrodynamic reductions of the kinetic equation for a soliton gas”, Theoret. and Math. Phys., 171:2 (2012), 675–682  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    9. Pavlov M.V., “Integrable Dispersive Chains and Energy Dependent Schrodinger Operator”, J. Phys. A-Math. Theor., 47:29 (2014), 295204  crossref  isi
    10. Maxim V. Pavlov, “Integrability of exceptional hydrodynamic-type systems”, Proc. Steklov Inst. Math., 302 (2018), 325–335  mathnet  crossref  crossref  isi  elib
    11. Marvan M. Pavlov M.V., “Integrable Dispersive Chains and Their Multi-Phase Solutions”, Lett. Math. Phys., 109:5 (2019), 1219–1245  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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