  We present an inverse scattering transform approach for the equation
$u_{txx}-3u_x+3u_xu_{xx}+uu_{xxx}=0$. 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.
