Geodesic
Canonicity of B\"acklund Transformation: $r$-Matrix Approach.~II
Informatics and Automation, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 134-139

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This work represents the second part of the paper devoted to the general proof of the canonicity of the Bäcklund transformation (BT) for Hamiltonian integrable systems described by an $SL(2)$-invariant $r$-matrix. Introducing an extended phase space from which the original space is obtained by imposing first-kind constraints, one can prove the canonicity of the BT by a new method. This new proof provides a natural explanation for the fact why the gauge transformation of the matrix $M$ associated with the BT has the same structure as the Lax operator $L$. This technique is illustrated through an example of a DST chain. 
@article{TRSPY_1999_226_a9,
     author = {E. K. Sklyanin},
     title = {Canonicity of {B\"acklund} {Transformation:} $r${-Matrix} {Approach.~II}},
     journal = {Informatics and Automation},
     pages = {134--139},
     publisher = {mathdoc},
     volume = {226},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_1999_226_a9/}
}
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E. K. Sklyanin. Canonicity of B\"acklund Transformation: $r$-Matrix Approach.~II. Informatics and Automation, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 134-139. http://geodesic.mathdoc.fr/item/TRSPY_1999_226_a9/