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Communications in Mathematical Physics

, Volume 141, Issue 1, pp 133–151 | Cite as

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

  • A. Degasperis
  • D. Lebedev
  • M. Olshanetsky
  • S. Pakuliak
  • A. Perelomov
  • P. Santini
Article

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Characteristic Property 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • A. Degasperis
    • 1
    • 2
  • D. Lebedev
    • 5
  • M. Olshanetsky
    • 3
  • S. Pakuliak
    • 4
  • A. Perelomov
    • 3
  • P. Santini
    • 1
    • 2
  1. 1.Dipartimento di FisicaUniversità La SapienzaRoma
  2. 2.INFN Sezione di RomaItaly
  3. 3.Institute for Theoretical and Experimental PhysicsMoscowUSSR
  4. 4.Institute for Theoretical PhysicsKievUSSR
  5. 5.Max-Planck-Institut für Mathematik and Physikalisches Institut der Universität BonnBonn 1Germany

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