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math.SP2013★ 22 cited
An inverse spectral problem related to the Geng-Xue two-component peakon equation
Hans Lundmark, Jacek Szmigielski
We solve a spectral and an inverse spectral problem arising in the computation of peakon solutions to the two-component PDE derived by Geng and Xue as a generalization of the Novik…
nlin.SI2013★ 1 cited
Shock creation and Painlevé property of colliding peakons in the Degasperis-Procesi Equation
Jacek Szmigielski, Lingjun Zhou
The Degasperis-Procesi equation (DP) is one of several equations known to model important nonlinear effects such as wave breaking and shock creation. It is, however, a special prop…
math-ph2013
Peakon-antipeakon interactions in the Degasperis-Procesi Equation
Jacek Szmigielski, Lingjun Zhou
Peakons are singular, soliton-like solutions to nonlinear wave equations whose dynamics can be studied using ordinary differential equations (ODEs). The Degasperis-Procesi equation…