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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
Dressing the Dressing Chain
Charalampos A. Evripidoua, Peter H. van der Kampa, Cheng Zhangb a Department of Mathematics and Statistics, La Trobe University,
Melbourne, Victoria 3086, Australia
b Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, China
Аннотация:
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 $n$.
Ключевые слова:
discrete dressing chain; lattice KdV; Darboux transformations; Liouville integrability.
Поступила: 18 апреля 2018 г.; в окончательном варианте 4 июня 2018 г.; опубликована 15 июня 2018 г.
Образец цитирования:
Charalampos A. Evripidou, Peter H. van der Kamp, Cheng Zhang, “Dressing the Dressing Chain”, SIGMA, 14 (2018), 059, 14 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1358 https://www.mathnet.ru/rus/sigma/v14/p59
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