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Dressing the Dressing Chain

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journal contribution
posted on 18.03.2022, 02:58 by Charalambos EvripidouCharalambos Evripidou, Pieter Van Der KampPieter Van Der Kamp, Cheng Zhang
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.

Funding

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).

History

Publication Date

15/06/2018

Journal

Symmetry Integrability and Geometry: Methods and Applications (SIGMA)

Volume

14

Article Number

059

Pagination

14p.

Publisher

Department of Applied Research, Institute of Mathematics of National Academy of Sciences of Ukraine

ISSN

1815-0659

Rights Statement

“The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License.”

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