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The Fredholm determinant method for discrete integrable evolution equations

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Abstract

The Fredholm determinant method defines in an explicit way a mapping from a linear evolution equation to a nonlinear soliton equation. Here, the method is extended to discrete soliton equations like the Toda and Langmuir lattice equations. Though the discrete version looks very similar to the continuous one, the proof is quite different. Explicit solution formulas are given, and the continuous limiting case is considered.

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Author notes

  1. Christoph Pöppe

    Present address: Until June 87: School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA

Authors and Affiliations

  1. Sektion mathematik, Friedrich-Schiller-Universität, DDR-6900, Jena, Germany

    Wolfgang Bauhardt

  2. Sonderforschungsbereich 123, Universität Heidelberg, Im Neuheimer Feld 294, D-6900, Heidelberg, Germany

    Christoph Pöppe

Authors
  1. Wolfgang Bauhardt
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  2. Christoph Pöppe
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Bauhardt, W., Pöppe, C. The Fredholm determinant method for discrete integrable evolution equations. Lett Math Phys 13, 167–178 (1987). https://doi.org/10.1007/BF00423443

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  • DOI: https://doi.org/10.1007/BF00423443

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