Multi-peakon solutions of the Degasperis–Procesi equation

We present an inverse scattering approach for computing n-peakon solutions of the Degasperis–Procesi equation (a modification of the Camassa–Holm (CH) shallow water equation). The associated non-self-adjoint spectral problem is shown to be amenable to analysis using the isospectral deformations induced from the n-peakon solution, and the inverse problem is solved by a method generalizing the continued fraction solution of the peakon sector of the CH equation.