Mathematics > Differential Geometry
[Submitted on 30 Nov 2021]
Title:Symplectic aspects of the tt*-Toda equations
View PDFAbstract: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 C. A. Tracy. 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.
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