On Certain Reductions of Integrable Equations on Symmetric Spaces.

We derive a Z2×Z2 reduced integrable system which is deeply connected with the famous Heisenberg ferromagnet equation. Its Lax pair is associated with the symmetric space SO(5)/SO(2)×SO(3). We study the spectral properties of the scattering operator, introduce the basic notions of its direct scattering problem and construct fundamental analytic solutions in terms of Volterra integral equations. We obtain recursion operator to describe the hierarchy of higher order equations associated with the same Lax operator L. [ABSTRACT FROM AUTHOR]