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TMF, 1980, Volume 45, Number 2, Pages 161–170 (Mi tmf3872)  

This article is cited in 6 scientific papers (total in 6 papers)

Complete integrability of dynamical systems generated by singular solutions of liouville's equation

A. K. Pogrebkov


Abstract: Variables of the action-angle type and the hamiltonian are constructed for a dynamical system of $N$ relativistic interacting particles the world lines of which coincide with the singular lines of the equation $\varphi_{tt}-\varphi_{xx}+(m^2/2)\exp\varphi=0$. The construction is performed in the usual one-time parametrization as well as in an arbitrary relativistic parametrization.

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English version:
Theoretical and Mathematical Physics, 1980, 45:2, 951–957

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Received: 28.12.1979

Citation: A. K. Pogrebkov, “Complete integrability of dynamical systems generated by singular solutions of liouville's equation”, TMF, 45:2 (1980), 161–170; Theoret. and Math. Phys., 45:2 (1980), 951–957

Citation in format AMSBIB
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\by A.~K.~Pogrebkov
\paper Complete integrability of~dynamical systems generated by~singular solutions of liouville's equation
\jour TMF
\yr 1980
\vol 45
\issue 2
\pages 161--170
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\zmath{https://zbmath.org/?q=an:0451.35084}
\transl
\jour Theoret. and Math. Phys.
\yr 1980
\vol 45
\issue 2
\pages 951--957
\crossref{https://doi.org/10.1007/BF01028591}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980LZ19000002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. P. Veselov, “Dynamics of the singularities of solutions of some nonlinear equations”, Theoret. and Math. Phys., 50:3 (1982), 314–316  mathnet  crossref  mathscinet  zmath  isi
    2. V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov, “Application of inverse scattering method to singular solutions of nonlinear equations. I”, Theoret. and Math. Phys., 53:2 (1982), 1051–1062  mathnet  crossref  mathscinet  isi
    3. S. V. Talalov, “Singular solutions of the Liouville equation on an interval”, Theoret. and Math. Phys., 67:3 (1986), 537–545  mathnet  crossref  mathscinet  zmath  isi
    4. Theoret. and Math. Phys., 104:1 (1995), 892–920  mathnet  crossref  mathscinet  zmath  isi
    5. B. Fuchssteiner, V. V. Tsegel'nik, “Analytical properties of solutions to a system of nonlinear partial differential equations”, Theoret. and Math. Phys., 105:2 (1995), 1354–1358  mathnet  crossref  mathscinet  zmath  isi
    6. S. V. Klimenko, I. N. Nikitin, “Singularities on world sheets of open relativistic strings”, Theoret. and Math. Phys., 114:3 (1998), 299–312  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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