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

Lundmark, Hans; Szmigielski, Jacek

Inverse Probl. 19, No. 6, 1241-1245 (2003).

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.

MSC:

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

Keywords:

Degasperis-Procesi equation; shallow water equation; \(n\)-peakon solution; continued fraction; Camassa-Holm equation