Multi-peakon solutions of the Degasperis–Procesi equation

By Hans Lundmark, Jacek Szmigielski. 2003

315 citations recorded by the source corpus.

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.

Subfields: Oceanography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7186c9d1f71f326b04e64257aa4f8b7c41565a1b

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In Oceanography

In Statistical and Nonlinear Physics

Citations in the corpus

Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation (2006, background): “Lundmark and Szmigielski [ 37 ] presented an inverse scattering approach for computing n-peakon solutions to Eq. (1.2).”
On the Blow-up Phenomena for the Degasperis–Procesi Equation (2010, background): “Recently, Lundmark and Szmigielski [31] presented an inverse scattering approach for computing n-peakon solutions to Eq.”
Traveling wave solutions of the Degasperis-Procesi equation (2005, background): “1) is the tence of multi-peakon solutions (an explicit formula for the two-peakon was presen [10]; other multi-peakons can also be obtained [17]) in analogy to the peakon soluti (1.”
ON THE UNIQUENESS OF DISCONTINUOUS SOLUTIONS TO THE DEGASPERIS–PROCESI EQUATION (2007, methodology): “[17] H. Lundmark and J. Szmigielski.”
Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation (2007, background): “Lundmark and Szmigielski [36] presented an inverse scattering approach for computing n-peakon solutions to the Degasperis-Procesi equation.”
Inverse scattering transform for the Degasperis–Procesi equation (2010, methodology): “ the mapping between the solution and the scattering data allows the interpretation of a generalised Fourier transform [1, 25, 26, 52]. The peakon solutions (peaked solitons) appear in the limit κ→ 0 [44], although such limit in the space of the scattering data will require further considerations. T”
On the well-posedness of the Degasperis-Procesi equation (2006, background): “Lundmark and Szmigielski [28] presented an inverse scattering approach for computing n-peakon solutions to (1.1).”
Global weak solutions and blow-up structure for the Degasperis–Procesi equation (2006, background): “Lundmark and Szmigielski [37] presented an inverse scattering approach for computing n-peakon solutions”
The Degasperis-Procesi equation on the half-line (2012, methodology): “e case on the half-line), the implementation of the IST to DP has proved to be more intricate. Nevertheless, an inverse scattering approach for computing the n-peakon solutions of DP was presented in [22], and it was recently shown in [8] (see also [4]) that the solution of the Cauchy problem on the”
Stability of peakons for the Degasperis‐Procesi equation (2007, background): “Recently, Lundmark and Szmigielski [26] presented an inverse scattering approach for computing n-peakon solutions to equation (1.”
A three-component generalization of Camassa–Holm equation with N-peakon solutions (2011, background): “The most attractive character of the CH equation is that in the case κ = 0, it admits peaked soliton solutions which are also called peakons and have been of great research interest [5,40,39, 3,4,18,36,37,29,30].”