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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

Bibliographic databases:

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
\Bibitem{BarNes83} \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 \mathnet{http://mi.mathnet.ru/tmf2203} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983SG66600003}