Restricted flows and the soliton equation with self-consistent sources
The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Bäcklund transformation for the restricted flows (by V.B. Kuznetsov et al.), we constructed two types of Darboux transf...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2006 |
| Main Authors: | , , |
| 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/123456789/146047 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Restricted flows and the soliton equation with self-consistent sources / Runliang Lin, Haishen Yao, Yunbo Zeng // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862715988054638592 |
|---|---|
| author | Runliang Lin Haishen Yao Yunbo Zeng |
| author_facet | Runliang Lin Haishen Yao Yunbo Zeng |
| citation_txt | Restricted flows and the soliton equation with self-consistent sources / Runliang Lin, Haishen Yao, Yunbo Zeng // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 19 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Bäcklund transformation for the restricted flows (by V.B. Kuznetsov et al.), we constructed two types of Darboux transformations for the KdV equation with self-consistent sources (KdVES). These Darboux transformations are used to get some explicit solutions of the KdVES, which include soliton, rational, positon, and negaton solutions.
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| first_indexed | 2025-12-07T18:02:00Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146047 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:02:00Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Runliang Lin Haishen Yao Yunbo Zeng 2019-02-06T15:01:07Z 2019-02-06T15:01:07Z 2006 Restricted flows and the soliton equation with self-consistent sources / Runliang Lin, Haishen Yao, Yunbo Zeng // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 19 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35Q51; 35Q53; 37K10 https://nasplib.isofts.kiev.ua/handle/123456789/146047 The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Bäcklund transformation for the restricted flows (by V.B. Kuznetsov et al.), we constructed two types of Darboux transformations for the KdV equation with self-consistent sources (KdVES). These Darboux transformations are used to get some explicit solutions of the KdVES, which include soliton, rational, positon, and negaton solutions. This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. The authors are grateful to the referees for the valuable comments. This work is supported by the Chinese Basic Research Project “Nonlinear Science”. R.L. Lin is supported in part by “Scientific Foundation for Returned Overseas Chinese Scholars, Ministry of Education”. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Restricted flows and the soliton equation with self-consistent sources Article published earlier |
| spellingShingle | Restricted flows and the soliton equation with self-consistent sources Runliang Lin Haishen Yao Yunbo Zeng |
| title | Restricted flows and the soliton equation with self-consistent sources |
| title_full | Restricted flows and the soliton equation with self-consistent sources |
| title_fullStr | Restricted flows and the soliton equation with self-consistent sources |
| title_full_unstemmed | Restricted flows and the soliton equation with self-consistent sources |
| title_short | Restricted flows and the soliton equation with self-consistent sources |
| title_sort | restricted flows and the soliton equation with self-consistent sources |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146047 |
| work_keys_str_mv | AT runlianglin restrictedflowsandthesolitonequationwithselfconsistentsources AT haishenyao restrictedflowsandthesolitonequationwithselfconsistentsources AT yunbozeng restrictedflowsandthesolitonequationwithselfconsistentsources |