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arXiv · 2111.15459

Symplectic aspects of the tt*-Toda equations

Ryosuke Odoi
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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 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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Ryosuke Odoi. 2021-11-30. Symplectic aspects of the tt*-Toda equations. https://doi.org/10.1088/1751-8121%2Fac59ff

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