Abstract
The \(\hat{A}_{2n}^{(2)}\)-hierarchy can be constructed from a splitting of the Kac–Moody algebra of type \(\hat{A}_{2n}^{(1)}\) by an involution. By choosing certain cross section of the gauge action, we obtain the \(\hat{A}_{2n}^{(2)}\)-KdV hierarchy. They are the equations for geometric invariants of isotropic curve flows of type A, which gives a geometric interpretation of the soliton hierarchy. In this paper, we construct Darboux and Bäcklund transformations for the \(\hat{A}_{2n}^{(2)}\)-hierarchy, and use it the construct Darboux transformations for the \(\hat{A}_{2n}^{(2)}\)-KdV hierarchy and isotropic curve flows of type A. Moreover, explicit soliton solutions for these hierarchies are given.
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Dedicated to Peter Li’s 70th Birthday.
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Z. Wu: Research supported in part by Guangdong Basic and Applied Basic Research Foundation (Grant No. 2021A1515010234) and Laboratory of Mathematics for Nonlinear Science, Fudan University.
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Terng, CL., Wu, Z. Darboux Transformations for the \(\hat{A}_{2n}^{(2)}\)-KdV Hierarchy. J Geom Anal 33, 111 (2023). https://doi.org/10.1007/s12220-022-01158-w
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DOI: https://doi.org/10.1007/s12220-022-01158-w