This article is cited in 23 papers

Lagrangian Chains and Canonical Bäcklund Transformations

V. E. Adler^a, V. G. Marikhin^b, A. B. Shabat<sup>b

a</sup> Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
^b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

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.

Received: 06.06.2001

DOI: 10.4213/tmf528

 English version: Theoretical and Mathematical Physics, 2001, 129:2, 1448–1465

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