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Nonlocal integrable partners to generalized MKdV and two-dimensional Toda lattice equation in the formalism of a dressing method with quantized spectral parameter

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Abstract

Two new hierarchies, MILW2 and a two-dimensional nonlocal Toda lattice are constructed. The characteristic property of the first one is the connection with the ILW2 hierarchy by means ofgl(2) Miura transformation. On the other hand, MILW2 equations turn out to be symmetry equations for a two-dimensional nonlocal Toda lattice. A new version of the dressing technique with quantized spectral parameter is proposed.

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Author notes

  1. D. Lebedev, M. Olshanetsky & A. Perelomov

    Present address: Institute for Theoretical and Experimental Physics, SU-117259, Moscow, USSR

Authors and Affiliations

  1. Dipartimento di Fisica, Università La Sapienza, P. le Aldo Moro 2, I-00185, Roma

    A. Degasperis & P. Santini

  2. INFN Sezione di Roma, Italy

    A. Degasperis & P. Santini

  3. Institute for Theoretical Physics, SU-252130, Kiev, USSR

    S. Pakuliak

  4. Max-Planck-Institut für Mathematik and Physikalisches Institut der Universität Bonn, W-5300, Bonn 1, Germany

    D. Lebedev

Authors
  1. A. Degasperis
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  2. D. Lebedev
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  3. M. Olshanetsky
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  4. S. Pakuliak
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  5. A. Perelomov
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  6. P. Santini
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Communicated by N. Yu. Reshetikhin

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Degasperis, A., Lebedev, D., Olshanetsky, M. et al. Nonlocal integrable partners to generalized MKdV and two-dimensional Toda lattice equation in the formalism of a dressing method with quantized spectral parameter. Commun.Math. Phys. 141, 133–151 (1991). https://doi.org/10.1007/BF02100008

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  • DOI: https://doi.org/10.1007/BF02100008

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