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Gauge Theory of Backlund Transformations, I

  • D. H. Sattinger
  • V. D. Zurkowski
Part of the NATO ASI Series book series (volume 37)

Abstract

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.

Keywords

Gauge Transformation Half Plane Riccati Equation Jump Condition Nonlinear Schrodinger Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • D. H. Sattinger
    • 1
  • V. D. Zurkowski
    • 1
  1. 1.University of MinnesotaUSA

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