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Factorization and Poisson correspondences

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Abstract

The Darboux transformation as an example of an integrable infinite-dimensional Poisson correspondence is discussed in the context of the general factorization problem. Generalizations related to energy-dependent Schrödinger operators and to Kac-Moody algebras are considered. We also present the finite-dimensional reductions of the Darboux transformation to stationary flows.

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Authors and Affiliations

  1. Department of Applied Mathematical Studies and Centre for Nonlinear Studies, University of Leeds, LS2 9JT, Leeds, UK

    A. P. Fordy

  2. Landau Institute for Theoretical Physics, ul. Kosygina 2, 117334, Moscow, Russia

    A. B. Shabat

  3. Department of Mathematics and Mechanics, Moscow State University, 119899, Moscow, Russia

    A. P. Veselov

Authors
  1. A. P. Fordy
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  2. A. B. Shabat
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  3. A. P. Veselov
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Dedicated to the memory of Ira Dorfman

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 2, pp. 225–245, November, 1995.

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Fordy, A.P., Shabat, A.B. & Veselov, A.P. Factorization and Poisson correspondences. Theor Math Phys 105, 1369–1386 (1995). https://doi.org/10.1007/BF02070933

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  • DOI: https://doi.org/10.1007/BF02070933

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