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TMF, 1983, Volume 56, Number 2, Pages 180–191 (Mi tmf2203)  

Bäcklund transformation for the Liouville equation and gauge conditions in the theory of a relativistic string

B. M. Barbashov, V. V. Nesterenko


Abstract: It is shown that the gauge conditions in the theory of a relativistic string, which make it possible to replace the nonlinear Liouville equation by the d'Alembert equation, are a direct consequence of the Bäcklund transformation relating the solutions of these equations. A purely geometrical derivation is given of the Bäcklund transformations for the Liouville equation. A classical theory of a relativistic string is constructed in the $t=\tau$ gauge using the moving frame formalism and exterior differential forms in the theory of surfaces. The moving frame on the string trajectory is chosen in a special way. As a result, the theory of a string in fourdimensional space-time reduces to the d'Alembert equation for a single scalar function.

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English version:
Theoretical and Mathematical Physics, 1983, 56:2, 752–760

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Received: 18.06.1982

Citation: B. M. Barbashov, V. V. Nesterenko, “Bäcklund transformation for the Liouville equation and gauge conditions in the theory of a relativistic string”, TMF, 56:2 (1983), 180–191; Theoret. and Math. Phys., 56:2 (1983), 752–760

Citation in format AMSBIB
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\by B.~M.~Barbashov, V.~V.~Nesterenko
\paper B\"acklund transformation for the Liouville equation and gauge conditions in the theory of a~relativistic string
\jour TMF
\yr 1983
\vol 56
\issue 2
\pages 180--191
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=718096}
\zmath{https://zbmath.org/?q=an:0536.58035|0551.58037}
\transl
\jour Theoret. and Math. Phys.
\yr 1983
\vol 56
\issue 2
\pages 752--760
\crossref{https://doi.org/10.1007/BF01016816}
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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