Planar radially symmetric Heisenberg spin system and generalized nonlinear Schrodinger equation: Gauge equivalence, Backlund transformations and explicit solutions

Abstract

Under suitable transformations, we show that the planar radially symmetric continuum Heisenberg ferromagnetic spin system and the geometrically equivalent generalized nonlinear Schrodinger equation (NLSE) are equivalent to a linearly x-dependent inhomogeneous spin system and generalized inhomogeneous NLSE respectively on a half-line. We construct appropriate Backlund transformations and indicate the construction of explicit solutions in the radially symmetric case.