Differential-geometric structures in the theory of two-dimensional integrable equations

The gauge representations of the integrable generalization of the Heisenberg magnet in (2+1)-dimensional space-time are interpreted in terms of topological charge. Restrictions on the class of solutions to the equation for a two-dimensional magnet are described for which it becomes gauge-equivalent to the Davy-Stuartson equation.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 189, pp. 75–81, 1991.The author is grateful to P. P. Kulish for stimulating discussions.