Ultradiscrete Painlevé VI with Parity Variables
We introduce a ultradiscretization with parity variables of the q-difference Painlevé VI system of equations. We show that ultradiscrete limit of Riccati-type solutions of q-Painlevé VI satisfies the ultradiscrete Painlevé VI system of equations with the parity variables, which is valid by using the...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2013 |
| Main Authors: | , |
| 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/123456789/149362 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Ultradiscrete Painlevé VI with Parity Variables / K. Takemura, T. Tsutsui / Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862546090415357952 |
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| author | Takemura, K. Tsutsui, T. |
| author_facet | Takemura, K. Tsutsui, T. |
| citation_txt | Ultradiscrete Painlevé VI with Parity Variables / K. Takemura, T. Tsutsui / Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We introduce a ultradiscretization with parity variables of the q-difference Painlevé VI system of equations. We show that ultradiscrete limit of Riccati-type solutions of q-Painlevé VI satisfies the ultradiscrete Painlevé VI system of equations with the parity variables, which is valid by using the parity variables. We study some solutions of the ultradiscrete Riccati-type equation and those of ultradiscrete Painlevé VI equation.
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| first_indexed | 2025-11-25T10:21:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149362 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T10:21:15Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Takemura, K. Tsutsui, T. 2019-02-21T07:16:16Z 2019-02-21T07:16:16Z 2013 Ultradiscrete Painlevé VI with Parity Variables / K. Takemura, T. Tsutsui / Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 13 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 39A13; 34M55; 37B15 DOI: http://dx.doi.org/10.3842/SIGMA.2013.070 https://nasplib.isofts.kiev.ua/handle/123456789/149362 We introduce a ultradiscretization with parity variables of the q-difference Painlevé VI system of equations. We show that ultradiscrete limit of Riccati-type solutions of q-Painlevé VI satisfies the ultradiscrete Painlevé VI system of equations with the parity variables, which is valid by using the parity variables. We study some solutions of the ultradiscrete Riccati-type equation and those of ultradiscrete Painlevé VI equation. The authors would like to thank Professor Junkichi Satsuma for discussions and suggestions.
 They also thank the referees for valuable comments. The first author is partially supported
 by the Grant-in-Aid for Young Scientists (B) (No. 22740107) from the Japan Society for the
 Promotion of Science. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Ultradiscrete Painlevé VI with Parity Variables Article published earlier |
| spellingShingle | Ultradiscrete Painlevé VI with Parity Variables Takemura, K. Tsutsui, T. |
| title | Ultradiscrete Painlevé VI with Parity Variables |
| title_full | Ultradiscrete Painlevé VI with Parity Variables |
| title_fullStr | Ultradiscrete Painlevé VI with Parity Variables |
| title_full_unstemmed | Ultradiscrete Painlevé VI with Parity Variables |
| title_short | Ultradiscrete Painlevé VI with Parity Variables |
| title_sort | ultradiscrete painlevé vi with parity variables |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149362 |
| work_keys_str_mv | AT takemurak ultradiscretepainleveviwithparityvariables AT tsutsuit ultradiscretepainleveviwithparityvariables |