Darboux transformations of the Camassa-Holm type systems

Shilong Huang and Hongmin Li

Chaos, Solitons & Fractals, 2022, vol. 157, issue C

Abstract: We propose a unified approach to establish Darboux-Bäcklund transformations of the Camassa-Holm (CH) type equations. The method simplifies the approach presented by Xia, Zhou and Qiao [J. Math. Phys. 57, 103502 (2016)] to obtain soliton solutions of the CH equation by the Darboux transformation, because it does not need to solve spectral problem of the CH equation at λ=0 which is a singular point in the auxiliary problem, and avoids computing asymptotic properties of the wave functions. We also study many other CH type equations such as the 2-CH, the modified CH, the Degasperis-Procesi and the Novikov via the method. Especially, we present three Bäcklund transformations of the 2-CH system.

Keywords: Camassa-Holm equation; Reciprocal transformation; Darboux transformation (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001205

DOI: 10.1016/j.chaos.2022.111910

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