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 TMF, 1983, Volume 57, Number 2, Pages 238–248 (Mi tmf2257)

Explicit solutions of $O(3)$ and $O(2,1)$ chiral models and the associated equations of the two-dimensional Toda chain and the Ernst equation when the solutions are parametrized by arbitrary functions

M. G. Tseitlin

Abstract: By means of elliptic solutions of the $O(3)$ and $O(2,1)$ $\sigma$ models parametrized by arbitrary holomorphie functions (generalization of a singular harmonic mapping) and the previously considered [1] correspondence between chiral models and systems with exponential interaction, elliptic solutions are obtained for one of the two-dimensional Toda chains corresponding to the Kac–Moody algebra parametrized by a holomorphie or an antiholomorphic function. Solutions of the sinh-Gordon equation are given. For the Ernst equation, a solution is generated by the meron sector of the $O(2,1)$ $\sigma$ model which is parametrized by two real functions (cylindrical waves) or a holomorphic function (stationary axisymmetric solutions). A solution of Liouville's equation on a torus is given.

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English version:
Theoretical and Mathematical Physics, 1983, 57:2, 1110–1117

Bibliographic databases:

Citation: M. G. Tseitlin, “Explicit solutions of $O(3)$ and $O(2,1)$ chiral models and the associated equations of the two-dimensional Toda chain and the Ernst equation when the solutions are parametrized by arbitrary functions”, TMF, 57:2 (1983), 238–248; Theoret. and Math. Phys., 57:2 (1983), 1110–1117

Citation in format AMSBIB
\Bibitem{Tse83}
\by M.~G.~Tseitlin
\paper Explicit solutions of~$O(3)$ and~$O(2,1)$ chiral models and the associated equations of the two-dimensional Toda chain and the Ernst equation when the solutions are parametrized by arbitrary functions
\jour TMF
\yr 1983
\vol 57
\issue 2
\pages 238--248
\mathnet{http://mi.mathnet.ru/tmf2257}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=734886}
\transl
\jour Theoret. and Math. Phys.
\yr 1983
\vol 57
\issue 2
\pages 1110--1117
\crossref{https://doi.org/10.1007/BF01018654}

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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. M. G. Tseitlin, “Solutions of two-dimensional einstein equations parametrized by arbitrary functions and generated by the O(2, 1) $\sigma$ model”, Theoret. and Math. Phys., 64:1 (1985), 679–686
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