Loop algebras and symmetries related to both a compact and a noncompact version of a (2+1)dimensional spin model
Abstract
We show that both the compact and the noncompact version of a nonlinear spin field system in 2 + 1 dimensions, the socalled Ishimori model, allows an infinitedimensional Lie algebra with a loop algebra structure. This feature seems characteristic of any integrable nonlinear field equation in 2 + 1 dimensions. We find also that the corresponding group transformations lead to a reduction procedure from which new solutions can be obtained from known ones.
 Publication:

Physics Letters B
 Pub Date:
 November 1991
 DOI:
 10.1016/03702693(91)900969
 Bibcode:
 1991PhLB..271..337P