Gauge equivalence of σ models with non-compact Grassmannian manifolds

The gauge equivalence (GE) of σ models associated with non-compact Grassmannian manifolds is investigated with emphasis on the necessary restrictions for the choice of gauge elements in such cases. The importance of GE in solving a non-linear system with the help of inverse scattering data of its gauge related counterpart is demonstrated. The gauge relations between generalised Landau-Lifshitz (LL) and non-linear Schroedinger (NLS) type equations and also between non-linear σ models and generalised 'sine-sinh-Gordon' equations for non-compact SU(p,q)/S(U(u,v) x U(s,t)) manifolds are established. Using H-gauge invariance of LL the GE is extended to some higher-order specific non-linear systems. The gauge connection among various LL and NLS equations are schematically represented. Along with the recovery of earlier results important new results, some with significant non-compact structures, are discovered. (author)