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 $3\times 3$-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.

arXiv comment61 pages, 11 figures