Geodesic
Lagrangian Chains and Canonical B\"acklund Transformations
Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 2, pp. 163-183

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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. 
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     author = {V. E. Adler and V. G. Marikhin and A. B. Shabat},
     title = {Lagrangian {Chains} and {Canonical} {B\"acklund} {Transformations}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {129},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_129_2_a0/}
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V. E. Adler; V. G. Marikhin; A. B. Shabat. Lagrangian Chains and Canonical B\"acklund Transformations. Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 2, pp. 163-183. http://geodesic.mathdoc.fr/item/TMF_2001_129_2_a0/