On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions
In this paper, we consider a reducible degeneration of a hyperelliptic curve of genus g. Using the Sato Grassmannian, we show that the limits of hyperelliptic solutions of the KP hierarchy exist and become soliton solutions of various types. We recover some results of Abenda, who studied regular sol...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2019 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210066 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions / A. Nakayashiki // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 23 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862738169021071360 |
|---|---|
| author | Nakayashiki, A. |
| author_facet | Nakayashiki, A. |
| citation_txt | On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions / A. Nakayashiki // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 23 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we consider a reducible degeneration of a hyperelliptic curve of genus g. Using the Sato Grassmannian, we show that the limits of hyperelliptic solutions of the KP hierarchy exist and become soliton solutions of various types. We recover some results of Abenda, who studied regular soliton solutions corresponding to a reducible rational curve obtained as a degeneration of a hyperelliptic curve. We study singular soliton solutions as well and clarify how the singularity structure of solutions is reflected in the matrices that determine soliton solutions.
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| first_indexed | 2025-12-07T21:24:15Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210066 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:15Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Nakayashiki, A. 2025-12-02T09:36:38Z 2019 On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions / A. Nakayashiki // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 23 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K40; 37K10; 14H70 arXiv: 1808.06748 https://nasplib.isofts.kiev.ua/handle/123456789/210066 https://doi.org/10.3842/SIGMA.2019.009 In this paper, we consider a reducible degeneration of a hyperelliptic curve of genus g. Using the Sato Grassmannian, we show that the limits of hyperelliptic solutions of the KP hierarchy exist and become soliton solutions of various types. We recover some results of Abenda, who studied regular soliton solutions corresponding to a reducible rational curve obtained as a degeneration of a hyperelliptic curve. We study singular soliton solutions as well and clarify how the singularity structure of solutions is reflected in the matrices that determine soliton solutions. The author would like to thank Simonetta Abenda, Yasuhiko Yamada for useful discussions. He is also grateful to Kanehisa Takasaki for comments on the manuscript of the paper and to Yuji Kodama for many inspiring questions and comments. This work is supported by JSPS Grants-in-Aid for Scientific Research No.15K04907. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions Article published earlier |
| spellingShingle | On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions Nakayashiki, A. |
| title | On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions |
| title_full | On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions |
| title_fullStr | On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions |
| title_full_unstemmed | On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions |
| title_short | On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions |
| title_sort | on reducible degeneration of hyperelliptic curves and soliton solutions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210066 |
| work_keys_str_mv | AT nakayashikia onreducibledegenerationofhyperellipticcurvesandsolitonsolutions |