English

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 utxx3ux+3uxuxx+uuxxx=0u_{txx}-3u_x+3u_xu_{xx}+uu_{xxx}=0. 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}
}