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Teoreticheskaya i Matematicheskaya Fizika, 1980, Volume 45, Number 3, Pages 365–376 (Mi tmf4342)  

This article is cited in 2 scientific papers (total in 2 papers)

Generalization of the model of a relativistic string in a geometrical approach

B. M. Barbashov, V. V. Nesterenko, A. M. Chervyakov
References:
Abstract: A model of a one-dimensionally extended relativistic object is proposed. Its dynamics is determined by the requirement that its covering surface in Minkowski space have constant mean curvature $h$ with respect to each normal direction. A special case of such surfaces is the world surface of a relativistic string (minimal surface with $h=0$). The methods of differential geometry are used to investigate the most interesting cases when the enveloping pseudo-Euclidean space-time has dimensions $D=3,4$. In the ease $D=3$, the proposed model is described by the single nonlinear equation $\square\varphi=h\sh\varphi$. In fourdimensional space-time, the dynamics of the model is determined by the system of two equations
$$ \square\varphi=\frac{1}{2}h(e^\varphi-e^{-\varphi}\cos\theta), \quad \square\theta=\frac{1}{2}he^{-\varphi}\sin\theta. $$
A Lax representation for this system is obtained in a geometrical approach, and the use of the inverse scattering technique is briefly discussed.
Received: 06.12.1979
English version:
Theoretical and Mathematical Physics, 1980, Volume 45, Issue 3, Pages 1082–1089
DOI: https://doi.org/10.1007/BF01016708
Bibliographic databases:
Language: Russian
Citation: B. M. Barbashov, V. V. Nesterenko, A. M. Chervyakov, “Generalization of the model of a relativistic string in a geometrical approach”, TMF, 45:3 (1980), 365–376; Theoret. and Math. Phys., 45:3 (1980), 1082–1089
Citation in format AMSBIB
\Bibitem{BarNesChe80}
\by B.~M.~Barbashov, V.~V.~Nesterenko, A.~M.~Chervyakov
\paper Generalization of the model of a~relativistic string in a~geometrical approach
\jour TMF
\yr 1980
\vol 45
\issue 3
\pages 365--376
\mathnet{http://mi.mathnet.ru/tmf4342}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=604533}
\zmath{https://zbmath.org/?q=an:0461.53018}
\transl
\jour Theoret. and Math. Phys.
\yr 1980
\vol 45
\issue 3
\pages 1082--1089
\crossref{https://doi.org/10.1007/BF01016708}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1980LZ77900007}
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  • https://www.mathnet.ru/eng/tmf4342
  • https://www.mathnet.ru/eng/tmf/v45/i3/p365
  • This publication is cited in the following 2 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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    References:50
    First page:2
     
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