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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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2019
Автор: Nakayashiki, A.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2019
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/210066
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-210066
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions
spellingShingle On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions
Nakayashiki, A.
title_short 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_sort on reducible degeneration of hyperelliptic curves and soliton solutions
author Nakayashiki, A.
author_facet Nakayashiki, A.
publishDate 2019
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/210066
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.
work_keys_str_mv AT nakayashikia onreducibledegenerationofhyperellipticcurvesandsolitonsolutions
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