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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.
MSC:
35R30Inverse problems for PDE
37K40Soliton theory, asymptotic behavior of solutions
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q58Other completely integrable PDE (MSC2000)
35P25Scattering theory (PDE)