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 |
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| Date: | 2019 |
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| 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| Summary: | 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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| ISSN: | 1815-0659 |