On the dynamics of the radially symmetric heisenberg ferromagnetic spin system

Abstract

By considering the geometrical equivalence of the radially symmetric Heisenberg ferromagnetic spin system in n-arbitrary spatial dimensions and the generalized nonlinear Schrodinger equation (GNLSE) with radial symmetry, it is shown that they possess the Painleve property only for the (n=2) circularly (planar radially) symmetric case. For the circularly symmetric case, suitable (2×2) matrix eigenvalue equations are constructed, involving nonisospectral flows and their gauge equivalence is shown. The connection with inhomogeneous systems and, in particular, the linearly x-dependent system is pointed out. Appropriate Backlund transformations (BT) and explicit soliton solutions for both the spin systems and the GNLSEs are also derived.