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.
|ジャーナル||Journal of Physics A: Mathematical and Theoretical|
|出版ステータス||Published - 2022 4月 22|
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