The Degasperis–Procesi equation on the half-line

We analyze a class of initial-boundary value problems for the Degasperis–Procesi equation on the half-line. Assuming that the solution u(x,t)u(x,t) exists, we show that it can be recovered from its initial and boundary values via the solution of a Riemann–Hilbert problem formulated in the plane of the complex spectral parameter kk.