The complex MKDV equation with step-like initial data: Large time asymptotic analysis

Abstract

In this paper, we study large-time asymptotics for the complex modified Korteveg–de Vries equation with step-like initial data. It is shown that the step-like initial problem can be described by a matrix Riemann–Hilbert problem. Further we apply the steepest descent method to obtain different large-time asymptotics in the Zakharov–Manakov region, a plane wave region, and a slow decay region.