Higher dimensional Degasperis–Procesi–Camassa–Holm systems

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.