Geodesic
Action as an~invariant of B\"acklund transformations for Lagrangian systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 71-78

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We construct a general theory of Bäcklund transformations for Lagrangian systems under the condition that the action is preserved by these transformations. We discuss the known Bäcklund transformations for classical soliton equations from the standpoint of this approach and obtain a new Bäcklund transformation for the Tzitzéica equation.
Keywords: integrable system, canonical transformation. 
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     author = {V. G. Marikhin},
     title = {Action as an~invariant of {B\"acklund} transformations for {Lagrangian} systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {71--78},
     publisher = {mathdoc},
     volume = {184},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a3/}
}
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V. G. Marikhin. Action as an~invariant of B\"acklund transformations for Lagrangian systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 71-78. http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a3/