Long-time asymptotics for the Degasperis-Procesi equation on the half-line

We analyze the long-time asymptotics for the Degasperis–Procesi equation on the half-line. By applying nonlinear steepest descent techniques to an associated $3\times 3$-matrix valued Riemann–Hilbert problem, we find an explicit formula for the leading order asymptotics of the solution in the similarity region in terms of the initial and boundary values.