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Theoretical and Mathematical Physics

, Volume 129, Issue 2, pp 1448–1465 | Cite as

Lagrangian Chains and Canonical Bäcklund Transformations

  • V. E. Adler
  • V. G. Marikhin
  • A. B. Shabat
Article

Abstract

We consider Darboux transformations for operators of arbitrary order and construct the general theory of Bäcklund transformations based on the Lagrangian formalism. The dressing chain for the Boussinesq equation and its reduction are demonstrative examples for the suggested general theory. We also discuss the well-known Bäcklund transformations for classical soliton equations.

Keywords

Soliton General Theory Arbitrary Order Lagrangian Formalism Boussinesq Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • V. E. Adler
    • 1
  • V. G. Marikhin
    • 2
  • A. B. Shabat
    • 2
  1. 1.Mathematical InstituteUfa Center, RASUfaRussia
  2. 2.Landau Institute for Theoretical Physics, RASMoscowRussia

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