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On Addition Formulae of KP, mKP and BKP Hierarchies
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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On Addition Formulae of KP, mKP and BKP Hierarchies
Інший ID:
2010 Mathematics Subject Classification: 14H70; 37K10; 37K20
DOI: http://dx.doi.org/10.3842/SIGMA.2013.035
DOI: http://dx.doi.org/10.3842/SIGMA.2013.035
Посилання:
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.
Підтримка:
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.
Дата:
2013
Переглядів:
473
Завантажень:
259
Анотація:
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.
