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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - E. K. Sklyanin
TI  - Canonicity of B\"acklund Transformation: $r$-Matrix Approach.~II
JO  - Informatics and Automation
PY  - 1999
SP  - 134
EP  - 139
VL  - 226
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_1999_226_a9/
LA  - ru
ID  - TRSPY_1999_226_a9
ER  - 
%0 Journal Article
%A E. K. Sklyanin
%T Canonicity of B\"acklund Transformation: $r$-Matrix Approach.~II
%J Informatics and Automation
%D 1999
%P 134-139
%V 226
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_1999_226_a9/
%G ru
%F TRSPY_1999_226_a9
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/

[1] Sklyanin E. K., “Canonicity of Bäcklund transformation: $r$-matrix approach, I”, AMS Collection dedicated to L. D. Faddeev seminar (to appear)

[2] Takhtadzhyan L. A., Faddeev L. D., Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl

[3] Kuznetsov V. B., Sklyanin E. K., “On Bäcklund transformations for many-body systems”, J. Phys. A: Math. Gen., 31 (1998), 2241–2251 | DOI | MR | Zbl

[4] Pasquier V., Gaudin M., “The periodic Toda chain and a matrix generalization of the Bessel function recursion relations”, J. Phys. A: Math. Gen., 25 (1992), 5243–5252 | DOI | MR | Zbl

[5] Baxter R. I., Exactly solved models in statistical mechanics, ch. 9–10, Acad. Press, London, 1982 | MR | Zbl