Abstract
The Pohlmeyer reduction is generalized for σ-models [Kahler, ℂp n, O(3)] in a twodimensional Euclidean space, possessing instanton solutions. The reduced equations are multidimensional generalizations of the Liouville equation [it is obtained by reduction from the ℂp 1 ∿O(3) model]. Solutions depending on 2n arbitrary analytic functions are computed for the equations obtained (n is the dimension of the manifold where the original system is specified). The connection with Painleve-type equations is noted.
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Literature cited
K. Pohlmeyer, “Integrable Hamiltonian systems and interactions through quadratic constraints,” Commun. Math. Phys.,46, 207–221 (1976).
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 101, pp. 186–202, 1982.
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Zeitlin, M.G. Pohlmeyer transformation in Euclidean space. J Math Sci 23, 2494–2499 (1983). https://doi.org/10.1007/BF01084178
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DOI: https://doi.org/10.1007/BF01084178