Higher dimensional Degasperis–Procesi–Camassa–Holm systems

Fa-ren Wang and S.Y. Lou

Chaos, Solitons & Fractals, 2023, vol. 174, issue C

Abstract: The (1+1)-dimensional models can be applied to derive corresponding higher dimensional models by a deformation algorithm with the help of their conservation laws, their Lax integrability can be proved in the same way. In this paper, we modify the original deformation algorithm such that the conserved density should not be derivative dependent. The modified deformation algorithm is mainly applied to the (1+1)-dimensional Degasperis-Procesi equation and Camassa–Holm equation to establish some brand-new (N+1)-dimensional coupled Degasperis–Procesi–Camassa–Holm systems and their (1+1)-dimensional reductions, whose Lax pairs have been given. On the other hand, we can find a new type of peakon solution of the (2+1)-dimensional deformed Degasperis-Procesi equation.

Keywords: Integable system; Deformation algorithm; Lax pair; Peakon solution; Coupled systems (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007683

DOI: 10.1016/j.chaos.2023.113867

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