Smooth Solutions of the tt* Equation: A Numerical Aided Case Study
An important special class of the tt* equations is the tt*-Toda equations. Guest et al. have given comprehensive studies on the tt*-Toda equations in a series of papers. The fine asymptotics for a large class of solutions of a special tt*-Toda equation, the case 4a in their classification, have been...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212250 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Smooth Solutions of the tt* Equation: A Numerical Aided Case Study. Yuqi Li. SIGMA 20 (2024), 057, 28 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862541911423713280 |
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| author | Li, Yuqi |
| author_facet | Li, Yuqi |
| citation_txt | Smooth Solutions of the tt* Equation: A Numerical Aided Case Study. Yuqi Li. SIGMA 20 (2024), 057, 28 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | An important special class of the tt* equations is the tt*-Toda equations. Guest et al. have given comprehensive studies on the tt*-Toda equations in a series of papers. The fine asymptotics for a large class of solutions of a special tt*-Toda equation, the case 4a in their classification, have been obtained in the paper [Comm. Math. Phys. 374 (2020), 923-973] in the series. Most of these formulas are obtained with elaborate reasoning, and the calculations involved are lengthy. There are concerns about these formulas if they have not been verified by other methods. The first part of this paper is devoted to the numerical verification of these fine asymptotics. In fact, the numerical studies can do more and should do more. A natural question is whether we can find more such beautiful formulas in the tt* equation via numerical study. The second part of this paper is devoted to the numerical study of the fine asymptotics of the solutions in an enlarged class defined from the Stokes data side. All the fine asymptotics of the solutions in the enlarged class are found by the numerical study. The success of the numerical study is largely due to the truncation structures of the tt* equation.
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| first_indexed | 2026-03-12T20:57:22Z |
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| id | nasplib_isofts_kiev_ua-123456789-212250 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-12T20:57:22Z |
| publishDate | 2024 |
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| spelling | Li, Yuqi 2026-02-03T07:53:49Z 2024 Smooth Solutions of the tt* Equation: A Numerical Aided Case Study. Yuqi Li. SIGMA 20 (2024), 057, 28 pages 1815-0659 2020 Mathematics Subject Classification: 33E17; 34E05; 35Q51; 65L05 arXiv:1910.13639 https://nasplib.isofts.kiev.ua/handle/123456789/212250 https://doi.org/10.3842/SIGMA.2024.057 An important special class of the tt* equations is the tt*-Toda equations. Guest et al. have given comprehensive studies on the tt*-Toda equations in a series of papers. The fine asymptotics for a large class of solutions of a special tt*-Toda equation, the case 4a in their classification, have been obtained in the paper [Comm. Math. Phys. 374 (2020), 923-973] in the series. Most of these formulas are obtained with elaborate reasoning, and the calculations involved are lengthy. There are concerns about these formulas if they have not been verified by other methods. The first part of this paper is devoted to the numerical verification of these fine asymptotics. In fact, the numerical studies can do more and should do more. A natural question is whether we can find more such beautiful formulas in the tt* equation via numerical study. The second part of this paper is devoted to the numerical study of the fine asymptotics of the solutions in an enlarged class defined from the Stokes data side. All the fine asymptotics of the solutions in the enlarged class are found by the numerical study. The success of the numerical study is largely due to the truncation structures of the tt* equation. Part of this work was done while Y. Li was visiting the Department of Mathematical Sciences of IUPUI. Y. Li would like to thank A. It's for his hospitality and the suggestion of verifying their formulas in [7, Corollary 8.3]. The work is partly supported by NSFC (12235007) and the Science and Technology Commission of Shanghai Municipality (No. 22DZ2229014). The author would also like to thank the referees for their helpful suggestions and comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Smooth Solutions of the tt* Equation: A Numerical Aided Case Study Article published earlier |
| spellingShingle | Smooth Solutions of the tt* Equation: A Numerical Aided Case Study Li, Yuqi |
| title | Smooth Solutions of the tt* Equation: A Numerical Aided Case Study |
| title_full | Smooth Solutions of the tt* Equation: A Numerical Aided Case Study |
| title_fullStr | Smooth Solutions of the tt* Equation: A Numerical Aided Case Study |
| title_full_unstemmed | Smooth Solutions of the tt* Equation: A Numerical Aided Case Study |
| title_short | Smooth Solutions of the tt* Equation: A Numerical Aided Case Study |
| title_sort | smooth solutions of the tt* equation: a numerical aided case study |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212250 |
| work_keys_str_mv | AT liyuqi smoothsolutionsofthettequationanumericalaidedcasestudy |