TY - JOUR
T1 - Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa III
T2 - Iwasawa Factorization and Asymptotics
AU - Guest, Martin A.
AU - Its, Alexander R.
AU - Lin, Chang Shou
N1 - Funding Information:
The first author was partially supported by JSPS Grant (A) 25247005, and the second author was partially supported by NSF Grant DMS-1361856. Both are grateful to Taida Institute for Mathematical Sciences for financial support and hospitality. We would like to express our sincere appreciation to Yuqi Li, who verified numerically all our asymptotic formulae, thereby revealing several errors in our original results. Numerical aspects of the tt*-Toda equations will be discussed by him in [19]. Independent numerical checks of our formulae were carried out by Robert Sinclair to a high degree of accuracy, and we are extremely grateful to him as well.
Funding Information:
The first author was partially supported by JSPS Grant (A) 25247005, and the second author was partially supported by NSF Grant DMS-1361856. Both are grateful to Taida Institute for Mathematical Sciences for financial support and hospitality. We would like to express our sincere appreciation to Yuqi Li, who verified numerically all our asymptotic formulae, thereby revealing several errors in our original results. Numerical aspects of the tt*-Toda equations will be discussed by him in [ 19 ]. Independent numerical checks of our formulae were carried out by Robert Sinclair to a high degree of accuracy, and we are extremely grateful to him as well.
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - This paper, the third in a series, completes our description of all (radial) solutions on C∗ of the tt*-Toda equations 2(wi)tt¯=-e2(wi+1-wi)+e2(wi-wi-1), using a combination of methods from p.d.e., isomonodromic deformations (Riemann–Hilbert method), and loop groups. We place these global solutions into the broader context of solutions which are smooth near 0. For such solutions, we compute explicitly the Stokes data and connection matrix of the associated meromorphic system, in the resonant cases as well as the non-resonant case. This allows us to give a complete picture of the monodromy data, holomorphic data, and asymptotic data of the global solutions.
AB - This paper, the third in a series, completes our description of all (radial) solutions on C∗ of the tt*-Toda equations 2(wi)tt¯=-e2(wi+1-wi)+e2(wi-wi-1), using a combination of methods from p.d.e., isomonodromic deformations (Riemann–Hilbert method), and loop groups. We place these global solutions into the broader context of solutions which are smooth near 0. For such solutions, we compute explicitly the Stokes data and connection matrix of the associated meromorphic system, in the resonant cases as well as the non-resonant case. This allows us to give a complete picture of the monodromy data, holomorphic data, and asymptotic data of the global solutions.
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U2 - 10.1007/s00220-019-03559-5
DO - 10.1007/s00220-019-03559-5
M3 - Article
AN - SCOPUS:85074483059
SN - 0010-3616
VL - 374
SP - 923
EP - 973
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -