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
Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 2, pp. 238-248
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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.
@article{TMF_1983_57_2_a6,
author = {M. G. Tseitlin},
title = {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},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {238--248},
publisher = {mathdoc},
volume = {57},
number = {2},
year = {1983},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1983_57_2_a6/}
}
TY - JOUR AU - M. G. Tseitlin TI - 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 JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1983 SP - 238 EP - 248 VL - 57 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1983_57_2_a6/ LA - ru ID - TMF_1983_57_2_a6 ER -
%0 Journal Article %A M. G. Tseitlin %T 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 %J Teoretičeskaâ i matematičeskaâ fizika %D 1983 %P 238-248 %V 57 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1983_57_2_a6/ %G ru %F TMF_1983_57_2_a6
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. Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 2, pp. 238-248. http://geodesic.mathdoc.fr/item/TMF_1983_57_2_a6/