Quadratic pseudopotentials for Gl(N,\({\mathbb{C}})\) principal sigma models (Q1069522)

The principal sigma model in two-dimensional Minkowski space is defined by the equation: \((g_ ug^{-1})_ v+(g_ vg^{-1})_ u=0\) where u and v are null coordinates, subscripts denote partial differentiations and g is a function with value in a Lie group G which in this case is taken to be Gl(n,\({\mathbb{C}})\), though the authors show that it can be easily generalized to Sl(n,\({\mathbb{C}})\). The authors derive matrix pseudopotentials for the problem choosing their structure to contain only quadratic nonlinearities of the Riccati type. The authors deduce the appropriate set of constraints which lead to the inner Bäcklund transformations. An iterated sequence of such Bäcklund transformations is explicitly solved by an inductive procedure. The appearance of singularities is analysed and a permutability theorem is demonstrated.