# Peakon-antipeakon interactions in the Degasperis-Procesi Equation

@article{Szmigielski2013PeakonantipeakonII, title={Peakon-antipeakon interactions in the Degasperis-Procesi Equation}, author={Jacek Szmigielski and Lingjun Zhou}, journal={arXiv: Mathematical Physics}, year={2013} }

Peakons are singular, soliton-like solutions to nonlinear wave equations whose dynamics can be studied using ordinary differential equations (ODEs). The Degasperis-Procesi equation (DP) is an important example of an integrable PDE exhibiting wave breaking in the peakon sector thus affording an interpretation of wave breaking as a mechanical collision of particles. In this paper we set up a general formalism in which to study collisions of DP peakons and apply it, as an illustration, to a…

## 14 Citations

### Colliding peakons and the formation of shocks in the Degasperis–Procesi equation

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2013

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 property of the DP…

### Dynamics of interlacing peakons (and shockpeakons) in the Geng-Xue equation

- Mathematics
- 2016

We consider multipeakon solutions, and to some extent also multishockpeakon solutions, of a coupled two-component integrable PDE found by Geng and Xue as a generalization of Novikov's cubically…

### A general family of multi-peakon equations and their properties

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2019

A general family of peakon equations is introduced, involving two arbitrary functions of the wave amplitude and the wave gradient. This family contains all of the known breaking wave equations,…

### A view of the peakon world through the lens of approximation theory

- MathematicsPhysica D: Nonlinear Phenomena
- 2022

### Shock creation and Painleve property of colliding peakons in the Degasperis-Procesi Equation

- Physics
- 2013

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 property of the DP…

### Lax Integrability and the Peakon Problem for the Modified Camassa–Holm Equation

- Mathematics
- 2017

Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. We show that the…

### Degasperis–Procesi peakon dynamical system and finite Toda lattice of CKP type

- MathematicsNonlinearity
- 2018

In this paper, we propose a finite Toda lattice of CKP type (C-Toda) together with a Lax pair. Our motivation is based on the fact that the Camassa–Holm (CH) peakon dynamical system and the finite…

### 2-Peakon Solutions and Non-uniqueness of the Fokas–Olver–Rosenau–Qiao Equation with Higher-Order Nonlinearity

- Materials ScienceBulletin of the Malaysian Mathematical Sciences Society
- 2022

For the Fokas–Olver–Rosenau–Qiao (FORQ) equation with higher-order nonlinearity, the multi-peakon solutions on the line was constructed by Anco and Recio in 2019. In this paper, we construct 2-peakon…

### New Phenomena in the World of Peaked Solitons

- Physics
- 2016

The aim of this work is to present new contributions to the theory of peaked solitons. The thesis consists of two papers,which are named “Newsolutionswith peakon creation in the Camassa–HolmandNovi…

### Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation

- MathematicsAdvances in Mathematical Physics
- 2021

For the generalized mCH equation, we construct a 2-peakon solution on both the line and the circle, and we can control the size of the initial data. The two peaks at different speeds move in the same…

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