Journal of Soviet Mathematics

, Volume 23, Issue 4, pp 2494–2499 | Cite as

Pohlmeyer transformation in Euclidean space

  • M. G. Zeitlin


The Pohlmeyer reduction is generalized for σ-models [Kahler, ℂpn, 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 ℂp1 ∿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.


Manifold Analytic Function Euclidean Space Original System Liouville Equation 
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Literature cited

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    K. Pohlmeyer, “Integrable Hamiltonian systems and interactions through quadratic constraints,” Commun. Math. Phys.,46, 207–221 (1976).Google Scholar
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    H. Eichenherr and K. Pohlmeyer, Preprint Universität Freiburg, THEP 79/6 (September, 1979); H. Eichenherr and J. Honerkamp, Preprint Universität Freiburg, THEP 79/12 (November, 1979).Google Scholar
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    A. M. Perelomov, “Instantons and Kähler manifolds,” Commun. Math. Phys.,63, 237–242 (1978).Google Scholar
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    A. N. Leznov, “On complete integrability of a nonlinear system of partial differential equations in two-dimensional space,” Teor. Mat. Fiz.,42, No. 3, 343–349 (1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • M. G. Zeitlin

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