Journal of Soviet Mathematics

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

Pohlmeyer transformation in Euclidean space

  • M. G. Zeitlin
Article
  • 21 Downloads

Abstract

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.

Keywords

Manifold Analytic Function Euclidean Space Original System Liouville Equation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    K. Pohlmeyer, “Integrable Hamiltonian systems and interactions through quadratic constraints,” Commun. Math. Phys.,46, 207–221 (1976).Google Scholar
  2. 2.
    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
  3. 3.
    A. M. Perelomov, “Instantons and Kähler manifolds,” Commun. Math. Phys.,63, 237–242 (1978).Google Scholar
  4. 4.
    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

There are no affiliations available

Personalised recommendations