We study a class of integrable non-linear differential equations related to
the A.III-type symmetric spaces. These spaces are realized as factor groups of
the form SU(N)/S(U(N-k) x U(k)). We use the Cartan involution corresponding to
this symmetric space as an element of the reduction group and restrict generic
Lax operators to this symmetric space. The symmetries of the Lax operator are
inherited by the fundamental analytic solutions and give a characterization of
the corresponding Riemann-Hilbert data.Comment: 14 pages, 1 figure, LaTeX iopart styl