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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
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  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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Theoretical and Mathematical Physics, 1983, 57:2, 1110–1117
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
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\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 Theoret. and Math. Phys.
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This publication is cited in the following articles:
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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