Exact asymmetric Skyrmion through generalized analytic functions

Skyrmion magnetic patterns in helimagnets is a subject of immense contemporary interest from both theoretical and experimental point of view [PRL'09a,'09b,'10, Science'09,Nature'10,'06,'03,'01].  However, the original idea of Skyrmions in 2d was put forward 40 years ego by Belavin and Polyakov (BP) [JETP'75], where exact Skyrmion solutions could be given by any analytic functions.

We propose an innovative extension of the BP solution for an anisotropic ferromagnet, based on a geometric (in-)equality with universal appeal, which takes the exact asymmetric solutions to a new class of complex  functions beyond analyticity, linking the Skyrmion to the contemporary d-bar problem, with potential of generalizing the conformal QFT models and related algebraic structures.  An application of our result in the construction of asymmetric Skyrmions, likely to be detected in precision experiments in helimagnets, is proposed.