# Dressing Method for the Degasperis-Procesi Equation

@article{Constantin2016DressingMF, title={Dressing Method for the Degasperis-Procesi Equation}, author={Adrian Constantin and R. Ivanov}, journal={Studies in Applied Mathematics}, year={2016}, volume={138}, pages={205-226} }

The soliton solutions of the Degasperis–Procesi equations are constructed by the implementation of the dressing method. The form of the one and two soliton solutions coincides with the form obtained by Hirota's method.

#### 24 Citations

A dressing method for soliton solutions of the Camassa-Holm equation

- Physics, Mathematics
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The soliton solutions of the Camassa-Holm equation are derived by the implementation of the dressing method. The form of the one and two soliton solutions coincides with the form obtained by other… Expand

Multisoliton solutions of the Degasperis–Procesi equation and its shortwave limit: Darboux transformation approach

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We propose a new approach for calculating multisoliton solutions of the Degasperis–Procesi equation and its shortwave limit by combining a reciprocal transformation with the Darboux transformation of… Expand

Camassa–Holm Cuspons, Solitons and Their Interactions via the Dressing Method

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- J. Nonlinear Sci.
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A dressing method is applied to a matrix Lax pair for the Camassa–Holm equation, thereby allowing for the construction of several global solutions of the system. In particular, solutions of system of… Expand

Bäcklund Transformations for the Degasperis-Procesi Equation

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We consider the Bäcklund transformation for the Degasperis-Procesi (DP) equation. Using the reciprocal transformation and the associated DP equation, we construct the Bäcklund transformation for the… Expand

Integrable negative flows of the Heisenberg ferromagnet equation hierarchy

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- The European Physical Journal Plus
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We study the negative flows of the hierarchy of the integrable Heisenberg ferromagnet model and their soliton solutions. The first negative flow is related to the so-called short pulse equation. We… Expand

Wave breaking analysis for the Fornberg–Whitham equation

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- Journal of Differential Equations
- 2018

Abstract In this paper, the wave breaking of the Fornberg–Whitham equation is studied. We first investigate the local well-posedness and show a blow-up scenario by local-in-time a priori estimates.… Expand

Reducible KAM Tori for the Degasperis–Procesi Equation

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- Communications in mathematical physics
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The main points are to exploit the integrability of the unperturbed equation, to look for special wave packet solutions and to perform a very careful algebraic analysis of the resonances. Expand

The stability of solutions for the Fornberg – Whitham equation in L 1 ( R ) space

- 2018

*Correspondence: Laishaoy@swufe.edu.cn 1Department of Mathematics, Southwestern University of Finance and Economics, Chengdu, China Abstract The L2(R) conservation law of solutions for the nonlinear… Expand

Exponential decay and symmetry of solitary waves to Degasperis-Procesi equation

- Mathematics
- 2019

We improve the decay argument by [Bona and Li, J. Math. Pures Appl., 1997] for solitary waves of general dispersive equations and illustrate it in the proof for the exponential decay of solitary… Expand

Liouville Correspondences between Integrable Hierarchies

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In this paper, we study explicit correspondences between the integrable Novikov and Sawada-Kotera hierarchies, and between the Degasperis-Procesi and Kaup-Kupershmidt hierarchies. We show how a pair… Expand

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