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GLM equations, tau function and scattering data

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Abstract

The direct and the inverse scattering problem for affine Toda/mKdV systems is addressed and is found to develop non-standard features within the framework of the inverse scattering method. A solution scheme based on the tau function formalism is described. The inverse problem is shown to be equivalent to a set of decoupled, scalar Gelfand-Levitan-Marchenko-type equations. The Fredholm-Grothendieck determinants of the latter are shown to define tau-functions in the sense of the Kyoto School. In particular, a simple monodromy formula allows the derivation of trace identities.

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  1. Max-Planck-Institut für Physik, Werner Heisenberg Institut, Föhringer Ring 6, D-80805, Munich, Germany

    Max R. Niedermaier

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  1. Max R. Niedermaier
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Communicated by R. H. Dijkgraaf

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Niedermaier, M.R. GLM equations, tau function and scattering data. Commun.Math. Phys. 160, 391–429 (1994). https://doi.org/10.1007/BF02103282

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