Symplectic aspects of the tt-Toda equations

Ryosuke Odoi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We evaluate explicitly, in terms of the asymptotic data, the ratio of the constant pre-factors in the large and small x asymptotics of the tau functions for global solutions of the tt∗-Toda equations. This constant problem for the sinh-Gordon equation, which is the case n = 1 of the tt∗-Toda equations, was solved by Tracy (1991 Commun. Math. Phys. 142 297-311). We also introduce natural symplectic structures on the space of asymptotic data and on the space of monodromy data for a wider class of solutions, and show that these symplectic structures are preserved by the Riemann-Hilbert correspondence.

Original languageEnglish
Article number165201
JournalJournal of Physics A: Mathematical and Theoretical
Issue number16
Publication statusPublished - 2022 Apr 22


  • Riemann-Hilbert correspondence
  • ttequations
  • τ-function

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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