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

DOI10.1134/S0040577920050049zbMath1460.76124OpenAlexW3031512270MaRDI QIDQ2193728

Gaihua Wang, Yonghui Kuang, Nianhua Li

Publication date: 20 August 2020

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577920050049

zbMATH Keywords

bi-Hamiltonian structureKaup-Kupershmidt flow hierarchynegative flowshortwave limit

Mathematics Subject Classification ID

Solitary waves for incompressible inviscid fluids (76B25) Soliton equations (35Q51)

Related Items

Smooth multisoliton solutions of a 2-component peakon system with cubic nonlinearity ⋮ A new 3-component Degasperis-Procesi hierarchy ⋮ A view of the peakon world through the lens of approximation theory ⋮ Darboux transformations of the Camassa-Holm type systems

Cites Work

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• Hamiltonian structures for the Ostrovsky-Vakhnenko equation
• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Cusp and loop soliton solutions of short-wave models for the Camassa-Holm and Degasperis-Procesi equations
• On a completely integrable nonlinear hyperbolic variational equation
• The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method.
• Propagation of ultra-short optical pulses in cubic nonlinear media
• The bi-Hamiltonian structure of the short pulse equation
• Darboux transformation and multi-soliton solutions of the Camassa-Holm equation and modified Camassa-Holm equation
• Multi-loop soliton solutions and their interaction in the Degasperis–Procesi equation
• Dressing Method for the Degasperis-Procesi Equation
• The multiple-soliton solution of the Camassa-Holm equation
• Inverse scattering transform for the Degasperis–Procesi equation
• The N -soliton solution of the Degasperis–Procesi equation
• Non-isospectral deformations and Darboux transformations for the third-order spectral problem
• Does the complex deformation of the Riemann equation exhibit shocks?
• Dynamics of Director Fields
• Solitons in a nonlinear model medium
• The two loop soliton solution of the Vakhnenko equation
• Third order spectral problems: reductions and Darboux transformations
• Wave Structure and Nonlinear Balances in a Family of Evolutionary PDEs
• Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves
• Multi-peakon solutions of the Degasperis–Procesi equation
• An integrable shallow water equation with peaked solitons
• Nonisospectral scattering problems: A key to integrable hierarchies
• The Short Pulse Equation Is Integrable
• On reduced CKP equations
• Prolongation algebras and Hamiltonian operators for peakon equations
• The determinant representation of an N-fold Darboux transformation for the short pulse equation
• Integrable semi-discretizations of the reduced Ostrovsky equation
• A Riemann–Hilbert approach for the Degasperis–Procesi equation
• Some Water Wave Equations and Integrability
• Smooth and singular multisoliton solutions of a modified Camassa–Holm equation with cubic nonlinearity and linear dispersion
• Degasperis-Procesi peakons and the discrete cubic string
• Multisoliton solutions of the Degasperis–Procesi equation and their peakon limit