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

Abstract

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 × 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.