Geodesic
Relativistic Toda Chains and Schlesinger Transformations
Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 2, pp. 209-224 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {R. I. Yamilov},
     title = {Relativistic {Toda} {Chains} and {Schlesinger} {Transformations}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2004_139_2_a2/}
}
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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/

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