Gauge Theory of Backlund Transformations, I
Backlund transformations are obtained as gauge transformations for Hamiltonian hierarchies over sl(2,C) for potentials in so(2) or su(2). The transformation of the scattering data is calculated, and it is shown how these transformations create or annihilate a pair of eigenvalues in the scattering data, hence create or annihilate a soliton in the potential Q. Repeated Backlund transformations are constructed which introduce higher order poles in the scattering data; and the structure of the higher order singularities is described. It is shown how an arbitrary set of poles in the scattering data may be removed by a sequence of Backlund transformations.
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