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TMF, 2004, Volume 139, Number 2, Pages 209–224 (Mi tmf60)  

This article is cited in 3 scientific papers (total in 3 papers)

Relativistic Toda Chains and Schlesinger Transformations

R. I. Yamilov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: 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, autotransformations

DOI: https://doi.org/10.4213/tmf60

Full text: PDF file (229 kB)
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English version:
Theoretical and Mathematical Physics, 2004, 139:2, 623–635

Bibliographic databases:

Received: 07.05.2003

Citation: R. I. Yamilov, “Relativistic Toda Chains and Schlesinger Transformations”, TMF, 139:2 (2004), 209–224; Theoret. and Math. Phys., 139:2 (2004), 623–635

Citation in format AMSBIB
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\paper Relativistic Toda Chains and Schlesinger Transformations
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\transl
\jour Theoret. and Math. Phys.
\yr 2004
\vol 139
\issue 2
\pages 623--635
\crossref{https://doi.org/10.1023/B:TAMP.0000026180.34362.c5}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yamilov R, “Symmetries as integrability criteria for differential difference equations”, Journal of Physics A-Mathematical and General, 39:45 (2006), R541–R623  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Levi D, Winternitz P, “Continuous symmetries of difference equations”, Journal of Physics A-Mathematical and General, 39:2 (2006), R1–R63  crossref  mathscinet  zmath  isi  scopus  scopus
    3. R. I. Yamilov, “Integrability conditions for an analogue of the relativistic Toda chain”, Theoret. and Math. Phys., 151:1 (2007), 492–504  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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