Geodesic
Relativistic Toda Chains and Schlesinger Transformations
Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 2, pp. 209-224

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

We construct the auto-Schlesinger transformations for all equations in the known list of integrable relativistic Toda chains. Our construction is essentially based on the equations being Lagrangian and on a standard transition to their Hamiltonian form; in this case, the transition is described by the changes of variables that are invertible but not pointwise. We discuss two examples of another type that has similar properties; these are also integrable Lagrangian equations allowing the Schlesinger transformation
Keywords: integrability, Toda chain, Lagrangian equations, Hamiltonian equations
Mots-clés : autotransformations. 
@article{TMF_2004_139_2_a2,
     author = {R. I. Yamilov},
     title = {Relativistic {Toda} {Chains} and {Schlesinger} {Transformations}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {209--224},
     publisher = {mathdoc},
     volume = {139},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_139_2_a2/}
}
TY  - JOUR
AU  - R. I. Yamilov
TI  - Relativistic Toda Chains and Schlesinger Transformations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2004
SP  - 209
EP  - 224
VL  - 139
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2004_139_2_a2/
LA  - ru
ID  - TMF_2004_139_2_a2
ER  - 
%0 Journal Article
%A R. I. Yamilov
%T Relativistic Toda Chains and Schlesinger Transformations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2004
%P 209-224
%V 139
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2004_139_2_a2/
%G ru
%F TMF_2004_139_2_a2
R. I. Yamilov. Relativistic Toda Chains and Schlesinger Transformations. Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 2, pp. 209-224. http://geodesic.mathdoc.fr/item/TMF_2004_139_2_a2/