Superposition of solutions to Bäcklund transformations for the SU(n) principal σ-model

We show that the Bäcklund transformations for the SU(n) principal σ-model may be linearized using a geometrical interpretation of these equations involving the minimal orbit of SU(n,n) in the Grassmann manifold G_n(C²ⁿ). Linearization puts the equations in Zakharov-Mikhailov-Shabat (ZMS) form. Using this form of the equations, we prove inductively a nonlinear superposition law and a permutability theorem for iterated Bäcklund transformations analogous to known results in the theory of the sine-Gordon and KdV equations. From the superposition law we get an explicit form for multisoliton solutions to the σ-model.