Dressing the Dressing Chain
The dressing chain is derived by applying Darboux transformations to the spectral problem of the Korteweg-de Vries (KdV) equation. It is also an auto-Bäcklund transformation for the modified KdV equation. We show that by applying Darboux transformations to the spectral problem of the dressing chain,...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209513 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Dressing the Dressing Chain / C.A. Evripidou, P.H. van der Kamp, C. Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862648231418134528 |
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| author | Evripidou, C.A. van der Kamp, P.H. Zhang, C. |
| author_facet | Evripidou, C.A. van der Kamp, P.H. Zhang, C. |
| citation_txt | Dressing the Dressing Chain / C.A. Evripidou, P.H. van der Kamp, C. Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The dressing chain is derived by applying Darboux transformations to the spectral problem of the Korteweg-de Vries (KdV) equation. It is also an auto-Bäcklund transformation for the modified KdV equation. We show that by applying Darboux transformations to the spectral problem of the dressing chain, one obtains the lattice KdV equation as the dressing chain of the dressing chain, and that the lattice KdV equation also arises as an auto-Bäcklund transformation for a modified dressing chain. In analogy to the results obtained for the dressing chain (Veselov and Shabat proved complete integrability for odd-dimensional periodic reductions), we study the (0,n)-periodic reduction of the lattice KdV equation, which is a two-valued correspondence. We provide explicit formulas for its branches and establish complete integrability for odd n.
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| first_indexed | 2025-12-07T14:34:35Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209513 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T14:34:35Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Evripidou, C.A. van der Kamp, P.H. Zhang, C. 2025-11-24T10:05:24Z 2018 Dressing the Dressing Chain / C.A. Evripidou, P.H. van der Kamp, C. Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35Q53; 37K05; 39A14 arXiv: 1804.02564 https://nasplib.isofts.kiev.ua/handle/123456789/209513 https://doi.org/10.3842/SIGMA.2018.059 The dressing chain is derived by applying Darboux transformations to the spectral problem of the Korteweg-de Vries (KdV) equation. It is also an auto-Bäcklund transformation for the modified KdV equation. We show that by applying Darboux transformations to the spectral problem of the dressing chain, one obtains the lattice KdV equation as the dressing chain of the dressing chain, and that the lattice KdV equation also arises as an auto-Bäcklund transformation for a modified dressing chain. In analogy to the results obtained for the dressing chain (Veselov and Shabat proved complete integrability for odd-dimensional periodic reductions), we study the (0,n)-periodic reduction of the lattice KdV equation, which is a two-valued correspondence. We provide explicit formulas for its branches and establish complete integrability for odd n. This work was supported by the Australian Research Council, by the China Strategy Implementation Grant Program of La Trobe University, by the NSFC (No. 11601312), and by the Shanghai Young Eastern Scholar program (2016-2019). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dressing the Dressing Chain Article published earlier |
| spellingShingle | Dressing the Dressing Chain Evripidou, C.A. van der Kamp, P.H. Zhang, C. |
| title | Dressing the Dressing Chain |
| title_full | Dressing the Dressing Chain |
| title_fullStr | Dressing the Dressing Chain |
| title_full_unstemmed | Dressing the Dressing Chain |
| title_short | Dressing the Dressing Chain |
| title_sort | dressing the dressing chain |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209513 |
| work_keys_str_mv | AT evripidouca dressingthedressingchain AT vanderkampph dressingthedressingchain AT zhangc dressingthedressingchain |