On Addition Formulae of KP, mKP and BKP Hierarchies

In this paper we study the addition formulae of the KP, the mKP and the BKP hierarchies. We prove that the total hierarchies are equivalent to the simplest equations of their addition formulae. In the case of the KP and the mKP hierarchies those results had previously been proved by Noumi, Takasaki...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2013
Main Author: Shigyo, Y.
Format: Article
Language:English
Published: Інститут математики НАН України 2013
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149208
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:On Addition Formulae of KP, mKP and BKP Hierarchies / Y. Shigyo // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 24 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Shigyo, Y.
author_facet Shigyo, Y.
citation_txt On Addition Formulae of KP, mKP and BKP Hierarchies / Y. Shigyo // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 24 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description In this paper we study the addition formulae of the KP, the mKP and the BKP hierarchies. We prove that the total hierarchies are equivalent to the simplest equations of their addition formulae. In the case of the KP and the mKP hierarchies those results had previously been proved by Noumi, Takasaki and Takebe by way of wave functions. Here we give alternative and direct proofs for the case of the KP and mKP hierarchies. Our method can equally be applied to the BKP hierarchy.
first_indexed 2025-12-07T18:00:17Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T18:00:17Z
publishDate 2013
publisher Інститут математики НАН України
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spelling Shigyo, Y.
2019-02-19T18:36:38Z
2019-02-19T18:36:38Z
2013
On Addition Formulae of KP, mKP and BKP Hierarchies / Y. Shigyo // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 24 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 14H70; 37K10; 37K20
DOI: http://dx.doi.org/10.3842/SIGMA.2013.035
https://nasplib.isofts.kiev.ua/handle/123456789/149208
In this paper we study the addition formulae of the KP, the mKP and the BKP hierarchies. We prove that the total hierarchies are equivalent to the simplest equations of their addition formulae. In the case of the KP and the mKP hierarchies those results had previously been proved by Noumi, Takasaki and Takebe by way of wave functions. Here we give alternative and direct proofs for the case of the KP and mKP hierarchies. Our method can equally be applied to the BKP hierarchy.
I would like to thank Masatoshi Noumi and Takashi Takebe for permitting me to see the
 manuscript [17] prior to its publication. I also thank Kanehisa Takasaki and Takashi Takebe
 for insightful comments and their interests in the present work. I also thank Yasuhiro Ohta and
 Soichi Okada for important comments about Pfaf fians and informing me about reference [9].
 Finally I am deeply grateful to Atsushi Nakayashiki for much advice. This research is supported
 by JSPS Grant-in-Aid for Scientific Research (B) No. 23340037.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
On Addition Formulae of KP, mKP and BKP Hierarchies
Article
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spellingShingle On Addition Formulae of KP, mKP and BKP Hierarchies
Shigyo, Y.
title On Addition Formulae of KP, mKP and BKP Hierarchies
title_full On Addition Formulae of KP, mKP and BKP Hierarchies
title_fullStr On Addition Formulae of KP, mKP and BKP Hierarchies
title_full_unstemmed On Addition Formulae of KP, mKP and BKP Hierarchies
title_short On Addition Formulae of KP, mKP and BKP Hierarchies
title_sort on addition formulae of kp, mkp and bkp hierarchies
url https://nasplib.isofts.kiev.ua/handle/123456789/149208
work_keys_str_mv AT shigyoy onadditionformulaeofkpmkpandbkphierarchies