On the dynamics of the radially symmetric Heisenberg ferromagnetic spin system
- 1 October 1991
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 32 (10) , 2923-2928
- https://doi.org/10.1063/1.529086
Abstract
By considering the geometrical equivalence of the radially symmetric Heisenberg ferromagnetic spin system in n‐arbitrary spatial dimensions and the generalized nonlinear Schrödinger equation (GNLSE) with radial symmetry, it is shown that they possess the Painlevé 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 Bäcklund transformations (BT) and explicit soliton solutions for both the spin systems and the GNLSEs are also derived.Keywords
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