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 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2013
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| 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| _version_ | 1862715752252964864 |
|---|---|
| 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.
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| first_indexed | 2025-12-07T18:00:17Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149208 |
| 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 |
| record_format | dspace |
| 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 published earlier |
| 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 |