The hyperbolic Heisenberg and sigma models in 1+1 dimensions

Hyperbolic versions of the integrable (1+1)-dimensional Heisenberg ferromagnet and sigma models are discussed in the context of topological solutions classificable by an integer “winding number.” Some explicit solutions are presented, and the existence of certain classes of such winding solutions is examined. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 122, No. 2, pp. 310–320, February, 2000.