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PreprintarXiv licencearXiv

Painlevé II connection problem revisited

  • Nikolai Iorgov
  • Oleg Lisovyy
  • Noam Tamarin
  • Yurii Zhuravlov
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Abstract

We study the inhomogeneous Painlevé II equation for generic monodromy data. Using Kapaev's asymptotic formulas, the parameters of Zak transform representations of the Painlevé II tau function on six special rays arg t=πp/3 (p=0,…,5) in the complex time plane are expressed in terms of Stokes parameters of the associated linear system. We then solve the connection problem for the tau function between these special rays, and provide analytical and numerical checks of our result.

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Cite

BibTeXRIS
BibTeX
@misc{iorgov2026painlevé,
  title = {{Painlevé II connection problem revisited}},
  author = {Nikolai Iorgov and Oleg Lisovyy and Noam Tamarin and Yurii Zhuravlov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28227},
  eprint = {2610.28227},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28227},
}
RIS
TY  - UNPB
TI  - Painlevé II connection problem revisited
AU  - Nikolai Iorgov
AU  - Oleg Lisovyy
AU  - Noam Tamarin
AU  - Yurii Zhuravlov
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28227
UR  - https://arxiv.org/abs/2610.28227
AB  - We study the inhomogeneous Painlevé II equation for generic monodromy data. Using Kapaev's asymptotic formulas, the parameters of Zak transform representations of the Painlevé II tau function on six special rays arg t=πp/3 (p=0,…,5) in the complex time plane are expressed in terms of Stokes parameters of the associated linear system. We then solve the connection problem for the tau function between these special rays, and provide analytical and numerical checks of our result.
ER  -