The Ostrovsky-Vakhnenko equation on the half-line: a Riemann-Hilbert approach

2015/08/30 by Xu Jian, Xu, Jian, Engui Fan +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1508.07556

openalex publication_date 2015/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze an initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line. This equation can be viewed as the short wave model for the Degasperis-Procesi (DP) equation. We show that the solution u(x,t) can be recovered from its initial and boundary values via the solution of a 3× 3 vector Riemann-Hilbert problem formulated in the complex plane of a spectral parameter z.

Related

• The Ostrovsky-Vakhnenko equation by a Riemann-Hilbert approach
• The Degasperis-Procesi equation on the half-line
• Soliton resolution and asymptotic stability of N-loop-soliton solutions for the Ostrovsky-Vakhnenko equation
• The unified method for the three-wave equation on the half-line
• A Riemann-Hilbert approach for the Degasperis-Procesi equation