On the Backlund transformation and the theorem of permutability for the generalized Weierstrass system

The connection between the structure of the second-order system describing the Euclidean sigma-model equations associated with the generalized Weierstrass system and the possibility of the construction of some classes of solutions is discussed. It is shown using the conditional symmetry method that the auto-Backlund transformation (auto-BT) for the generalized Weierstrass system can be constructed. The permutability theorem for this auto-BT is formulated. New classes of nonsplitting multisoliton solutions are obtained through the use of the theorem of permutability.