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Darboux transformations of the Camassa-Holm type systems

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  • Huang, Shilong
  • Li, Hongmin

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.

Suggested Citation

  • Huang, Shilong & Li, Hongmin, 2022. "Darboux transformations of the Camassa-Holm type systems," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001205
    DOI: 10.1016/j.chaos.2022.111910
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