Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation
For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations. The reduction of one of the Bäcklund-Darboux transform...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2014
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146690 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation / L.L. Xue, Q.P. Liu // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 20 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862713179161755648 |
|---|---|
| author | Xue, L.L. Liu, Q.P. |
| author_facet | Xue, L.L. Liu, Q.P. |
| citation_txt | Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation / L.L. Xue, Q.P. Liu // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations. The reduction of one of the Bäcklund-Darboux transformations and the corresponding discrete system are considered for Kupershmidt's super KdV equation. When all the odd variables vanish, a nonlinear superposition formula is obtained for Levi's Bäcklund transformation for the KdV equation.
|
| first_indexed | 2025-12-07T17:42:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146690 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:42:28Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Xue, L.L. Liu, Q.P. 2019-02-10T18:56:56Z 2019-02-10T18:56:56Z 2014 Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation / L.L. Xue, Q.P. Liu // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35Q53; 37K10; 35A30 DOI:10.3842/SIGMA.2014.045 https://nasplib.isofts.kiev.ua/handle/123456789/146690 For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations. The reduction of one of the Bäcklund-Darboux transformations and the corresponding discrete system are considered for Kupershmidt's super KdV equation. When all the odd variables vanish, a nonlinear superposition formula is obtained for Levi's Bäcklund transformation for the KdV equation. The comments of the anonymous referees have been useful in clarifying certain points such as the
 connection between Levi’s B¨acklund transformation and elementary B¨acklund transformation of
 the KdV equation. This work is supported by the National Natural Science Foundation of China
 (grant numbers: 10971222, 11271366 and 11331008) and the Fundamental Research Funds for
 Central Universities. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation Article published earlier |
| spellingShingle | Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation Xue, L.L. Liu, Q.P. |
| title | Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation |
| title_full | Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation |
| title_fullStr | Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation |
| title_full_unstemmed | Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation |
| title_short | Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation |
| title_sort | bäcklund-darboux transformations and discretizations of super kdv equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146690 |
| work_keys_str_mv | AT xuell backlunddarbouxtransformationsanddiscretizationsofsuperkdvequation AT liuqp backlunddarbouxtransformationsanddiscretizationsofsuperkdvequation |