Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation
The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota-Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary Darboux transformations are derived for the discrete potential mo...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148634 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation / Y. Shi, J. Nimmo, J. Zhao // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862713885766713344 |
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| author | Shi, Y. Nimmo, J. Zhao, J. |
| author_facet | Shi, Y. Nimmo, J. Zhao, J. |
| citation_txt | Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation / Y. Shi, J. Nimmo, J. Zhao // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota-Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary Darboux transformations are derived for the discrete potential modified KdV equation and it is shown how these may be used to construct exact solutions.
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| first_indexed | 2025-12-07T17:47:42Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148634 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:47:42Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Shi, Y. Nimmo, J. Zhao, J. 2019-02-18T16:48:08Z 2019-02-18T16:48:08Z 2017 Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation / Y. Shi, J. Nimmo, J. Zhao // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 21 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 39A14; 37K10; 35C08 DOI:10.3842/SIGMA.2017.036 https://nasplib.isofts.kiev.ua/handle/123456789/148634 The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota-Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary Darboux transformations are derived for the discrete potential modified KdV equation and it is shown how these may be used to construct exact solutions. One of the author (YS) would like to acknowledge Professor Jarmo Hietarinta for his useful suggestions and hospitality when the author visited Turku University. The authors (YS and JXZ) also thank for the financial support from NSFC (Grant Numbers 11501510, 11271362, 11271266). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation Article published earlier |
| spellingShingle | Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation Shi, Y. Nimmo, J. Zhao, J. |
| title | Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation |
| title_full | Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation |
| title_fullStr | Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation |
| title_full_unstemmed | Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation |
| title_short | Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation |
| title_sort | darboux and binary darboux transformations for discrete integrable systems. ii. discrete potential mkdv equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148634 |
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