## Abstract

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 language | English |
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Article number | 165201 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 55 |

Issue number | 16 |

DOIs | |

Publication status | Published - 2022 Apr 22 |

## Keywords

- 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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