THE OSTROVSKY–VAKHNENKO EQUATION BY A RIEMANN–HILBERT APPROACH

Abstract

Abstract. We present an inverse scattering transform approach for the equation utxx − 3ux + 3uxuxx + uuxxx = 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. 1.