An integrable semi-discrete Degasperis-Procesi equation

2015/10/11 by Bao‐Feng Feng, Feng, Bao-Feng, Ken‐ichi Maruno +3 · 2 citations
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS)

paper · pdf · doi:10.48550/arxiv.1510.03010

openalex publication_date 2015/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on our previous work to the Degasperis-Procesi equation (J. Phys. A 46 045205) and the integrable semi-discrete analogue of its short wave limit (J. Phys. A 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota's bilinear method. Meanwhile, N-soliton solution to the semi-discrete Degasperis-Procesi equation is provided and proved. It is shown that the proposed semi-discrete Degasperis-Procesi equation, along with its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuous limit.

Citations

• The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations

Cited by

• Integrable Deformation of Space Curves, Generalized Heisenberg Ferromagnet Equation and Two-Component Modified Camassa-Holm Equation
• Integrable self-adaptive moving mesh schemes for multi-component short pulse type equations under general boundary conditions

Related

• Soliton resolution and asymptotic stability of N-solitons to the Degasperis-Procesi equation on the line
• Soliton dynamics for the general Degasperis-Procesi equation
• Solitons and peaked solitons for the general Degasperis-Procesi model
• Spectral stability of smooth solitary waves for the Degasperis-Procesi Equation
• The Cauchy problem for the Degasperis-Procesi Equation: Painlevé Asymptotics in Transition Zones