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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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2013-04-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2013.035 |
| _version_ | 1818366318213070848 |
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| author | Yoko Shigyo |
| author_facet | Yoko Shigyo |
| author_sort | Yoko Shigyo |
| collection | DOAJ |
| 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 | 2024-12-13T22:34:15Z |
| format | Article |
| id | doaj.art-8967b023a9444dbbb991c25c51f23e1c |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-13T22:34:15Z |
| publishDate | 2013-04-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-8967b023a9444dbbb991c25c51f23e1c2022-12-21T23:29:00ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592013-04-01903510.3842/SIGMA.2013.035On Addition Formulae of KP, mKP and BKP HierarchiesYoko ShigyoIn 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.http://dx.doi.org/10.3842/SIGMA.2013.035KP hierarchymodified KP hierarchyBKP hierarchy |
| spellingShingle | Yoko Shigyo On Addition Formulae of KP, mKP and BKP Hierarchies Symmetry, Integrability and Geometry: Methods and Applications KP hierarchy modified KP hierarchy BKP hierarchy |
| 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 |
| topic | KP hierarchy modified KP hierarchy BKP hierarchy |
| url | http://dx.doi.org/10.3842/SIGMA.2013.035 |
| work_keys_str_mv | AT yokoshigyo onadditionformulaeofkpmkpandbkphierarchies |