Multi-peakon solutions of the Degasperis-Procesi equation. (English) Zbl 1041.35090

Summary: 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.


35R30 Inverse problems for PDEs
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q58 Other completely integrable PDE (MSC2000)
35P25 Scattering theory for PDEs
Full Text: DOI arXiv