The Ostrovsky-Vakhnenko equation by a Riemann-Hilbert approach
Exactly Solvable and Integrable Systems
2013-11-05 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We present an inverse scattering transform approach for the equation . This equation can be viewed as the short wave model for the Degasperis-Procesi equation or the differentiated Ostrovsky-Vakhnenko equation. The approach is based on an associated Riemann-Hilbert problem, which allows us to give a representation for the classical (smooth) solution, to get the principal term of its long time asymptotics, and also to describe loop soliton solutions.
Keywords
Cite
@article{arxiv.1311.0495,
title = {The Ostrovsky-Vakhnenko equation by a Riemann-Hilbert approach},
author = {Anne Boutet de Monvel and Dmitry Shepelsky},
journal= {arXiv preprint arXiv:1311.0495},
year = {2013}
}