On the Riemann–Hilbert problem for the reverse space-time nonlocal Hirota equation with step-like initial data

Abstract In this paper, we use the Riemann–Hilbert (RH) method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data: q ( z , 0) = o (1) as z → −∞ and q ( z , 0) = δ + o (1) as z → ∞, where δ is an arbitrary positive constant. We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameter λ . As an example, we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.