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

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Abstract
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 Gn (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.