Bäcklund-Darboux Transformations for Super KdV Type Equations
By introducing a Miura transformation, we derive a generalized super modified Korteweg-de Vries (gsmKdV) equation from the generalized super KdV (gsKdV) equation. It is demonstrated that, while the gsKdV equation takes Kupershmidt's super KdV (sKdV) equation and Geng-Wu's sKdV equation as...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2025 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2025
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/213526 |
| 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 for Super KdV Type Equations. Lingling Xue, Shasha Wang and Qing Ping Liu. SIGMA 21 (2025), 050, 22 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862575425899724800 |
|---|---|
| author | Xue, Lingling Wang, Shasha Liu, Qing Ping |
| author_facet | Xue, Lingling Wang, Shasha Liu, Qing Ping |
| citation_txt | Bäcklund-Darboux Transformations for Super KdV Type Equations. Lingling Xue, Shasha Wang and Qing Ping Liu. SIGMA 21 (2025), 050, 22 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | By introducing a Miura transformation, we derive a generalized super modified Korteweg-de Vries (gsmKdV) equation from the generalized super KdV (gsKdV) equation. It is demonstrated that, while the gsKdV equation takes Kupershmidt's super KdV (sKdV) equation and Geng-Wu's sKdV equation as two distinct reductions, there are also two equations, namely Kupershmidt's super modified KdV (smKdV) equation and Hu's smKdV equation, which are associated with the gsmKdV equation. By analyzing the flows within the gsKdV and gsmKdV hierarchies, we specifically derive the first negative flows associated with both hierarchies. We then construct several Bäcklund-Darboux transformations (BDTs) for both the gsKdV and gsmKdV equations, elucidating the interrelationship between them. By proper reductions, we are able not only to recover the previously known BDTs for Kupershimdt's sKdV and smKdV equations, but also to obtain the BDTs for Geng-Wu's sKdV/smKdV and Hu's smKdV equations. As applications, we construct some exact solutions for those equations. Since all flows of the sKdV or smKdV hierarchy share the same spatial parts of the spectral problem, these Darboux matrices and spatial parts of BTs apply to any flow of those hierarchies.
|
| first_indexed | 2026-03-21T12:06:21Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213526 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T12:06:21Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Xue, Lingling Wang, Shasha Liu, Qing Ping 2026-02-18T11:25:15Z 2025 Bäcklund-Darboux Transformations for Super KdV Type Equations. Lingling Xue, Shasha Wang and Qing Ping Liu. SIGMA 21 (2025), 050, 22 pages 1815-0659 2020 Mathematics Subject Classification: 35Q53; 35A30; 58J72 arXiv:2410.21878 https://nasplib.isofts.kiev.ua/handle/123456789/213526 https://doi.org/10.3842/SIGMA.2025.050 By introducing a Miura transformation, we derive a generalized super modified Korteweg-de Vries (gsmKdV) equation from the generalized super KdV (gsKdV) equation. It is demonstrated that, while the gsKdV equation takes Kupershmidt's super KdV (sKdV) equation and Geng-Wu's sKdV equation as two distinct reductions, there are also two equations, namely Kupershmidt's super modified KdV (smKdV) equation and Hu's smKdV equation, which are associated with the gsmKdV equation. By analyzing the flows within the gsKdV and gsmKdV hierarchies, we specifically derive the first negative flows associated with both hierarchies. We then construct several Bäcklund-Darboux transformations (BDTs) for both the gsKdV and gsmKdV equations, elucidating the interrelationship between them. By proper reductions, we are able not only to recover the previously known BDTs for Kupershimdt's sKdV and smKdV equations, but also to obtain the BDTs for Geng-Wu's sKdV/smKdV and Hu's smKdV equations. As applications, we construct some exact solutions for those equations. Since all flows of the sKdV or smKdV hierarchy share the same spatial parts of the spectral problem, these Darboux matrices and spatial parts of BTs apply to any flow of those hierarchies. We thank the anonymous referees for their useful comments. This work is supported by the National Natural Science Foundation of China (Grant Nos. 12175111, 11931107, and 12171474), NSFC-RFBR (Grant No. 12111530003), and the K.C. Wong Magna Fund in Ningbo University. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Bäcklund-Darboux Transformations for Super KdV Type Equations Article published earlier |
| spellingShingle | Bäcklund-Darboux Transformations for Super KdV Type Equations Xue, Lingling Wang, Shasha Liu, Qing Ping |
| title | Bäcklund-Darboux Transformations for Super KdV Type Equations |
| title_full | Bäcklund-Darboux Transformations for Super KdV Type Equations |
| title_fullStr | Bäcklund-Darboux Transformations for Super KdV Type Equations |
| title_full_unstemmed | Bäcklund-Darboux Transformations for Super KdV Type Equations |
| title_short | Bäcklund-Darboux Transformations for Super KdV Type Equations |
| title_sort | bäcklund-darboux transformations for super kdv type equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213526 |
| work_keys_str_mv | AT xuelingling backlunddarbouxtransformationsforsuperkdvtypeequations AT wangshasha backlunddarbouxtransformationsforsuperkdvtypeequations AT liuqingping backlunddarbouxtransformationsforsuperkdvtypeequations |