Pohlmeyer transformation in Euclidean space
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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.
KeywordsManifold Analytic Function Euclidean Space Original System Liouville Equation
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