TY - JOUR

T1 - Symplectic aspects of the tt∗-Toda equations

AU - Odoi, Ryosuke

N1 - Funding Information:
This work is part of the author’s PhD thesis at Waseda University. He would like to acknowledge his supervisor, Professor Martin Guest for his support throughout this work and his guidance in this field. He would like to acknowledge Professor Alexander Its for his friendly advice and his suggestions regarding the constant problem. He is also glad to acknowledge the financial support from the mathematics and physics unit ‘multiscale analysis, modelling and simulation’, top global university project, Waseda University.
Publisher Copyright:
© 2022 IOP Publishing Ltd.

PY - 2022/4/22

Y1 - 2022/4/22

N2 - 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.

AB - 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.

KW - Riemann-Hilbert correspondence

KW - ttequations

KW - τ-function

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U2 - 10.1088/1751-8121/ac59ff

DO - 10.1088/1751-8121/ac59ff

M3 - Article

AN - SCOPUS:85128174738

SN - 1751-8113

VL - 55

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 16

M1 - 165201

ER -