Dispersionless Hirota Equations of Two-Component BKP Hierarchy
The BKP hierarchy has a two-component analogue (the 2-BKP hierarchy). Dispersionless limit of this multi-component hierarchy is considered on the level of the τ-function. The so called dispersionless Hirota equations are obtained from the Hirota equations of the τ-function. These dispersionless Hiro...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2006 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146164 |
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| Cite this: | Dispersionless Hirota Equations of Two-Component BKP Hierarchy / K. Takasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 30 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-146164 |
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Takasaki, K. 2019-02-07T19:55:15Z 2019-02-07T19:55:15Z 2006 Dispersionless Hirota Equations of Two-Component BKP Hierarchy / K. Takasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 30 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35Q58; 37K10; 58F07 https://nasplib.isofts.kiev.ua/handle/123456789/146164 The BKP hierarchy has a two-component analogue (the 2-BKP hierarchy). Dispersionless limit of this multi-component hierarchy is considered on the level of the τ-function. The so called dispersionless Hirota equations are obtained from the Hirota equations of the τ-function. These dispersionless Hirota equations turn out to be equivalent to a system of Hamilton-Jacobi equations. Other relevant equations, in particular, dispersionless Lax equations, can be derived from these fundamental equations. For comparison, another approach based on auxiliary linear equations is also presented. I would like to thank T. Ikeda, T. Shiota and T. Takebe for cooperation. I also would like to thank L. Martinez Alonso, B. Konopelchenko, M. Ma˜nas and A. Sorin for useful discussions during the SISSA conference “Riemann–Hilbert Problems, Integrability and Asymptotics” in September, 2005. This research was partially supported by Grant-in-Aid for Scientific Research No. 16340040 from the Japan Society for the Promotion of Science. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dispersionless Hirota Equations of Two-Component BKP Hierarchy Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Dispersionless Hirota Equations of Two-Component BKP Hierarchy |
| spellingShingle |
Dispersionless Hirota Equations of Two-Component BKP Hierarchy Takasaki, K. |
| title_short |
Dispersionless Hirota Equations of Two-Component BKP Hierarchy |
| title_full |
Dispersionless Hirota Equations of Two-Component BKP Hierarchy |
| title_fullStr |
Dispersionless Hirota Equations of Two-Component BKP Hierarchy |
| title_full_unstemmed |
Dispersionless Hirota Equations of Two-Component BKP Hierarchy |
| title_sort |
dispersionless hirota equations of two-component bkp hierarchy |
| author |
Takasaki, K. |
| author_facet |
Takasaki, K. |
| publishDate |
2006 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
The BKP hierarchy has a two-component analogue (the 2-BKP hierarchy). Dispersionless limit of this multi-component hierarchy is considered on the level of the τ-function. The so called dispersionless Hirota equations are obtained from the Hirota equations of the τ-function. These dispersionless Hirota equations turn out to be equivalent to a system of Hamilton-Jacobi equations. Other relevant equations, in particular, dispersionless Lax equations, can be derived from these fundamental equations. For comparison, another approach based on auxiliary linear equations is also presented.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146164 |
| fulltext |
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| citation_txt |
Dispersionless Hirota Equations of Two-Component BKP Hierarchy / K. Takasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 30 назв. — англ. |
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AT takasakik dispersionlesshirotaequationsoftwocomponentbkphierarchy |
| first_indexed |
2025-11-24T12:50:23Z |
| last_indexed |
2025-11-24T12:50:23Z |
| _version_ |
1850846746198933504 |