Long-time asymptotics for the defocusing Hirota equation with finite density initial data

Abstract – Using the Riemann–Hilbert (RH) formulation of the Cauchy problem together with the (Formula presented)-generalized nonlinear steepest descent method, we derive the long-time asymptotics of the defocusing Hirota equation in the oscillatory regime. For (Formula presented), four phase points lie on the jump contour (Formula presented), yielding the asymptotic expansion (Formula presented) Here, the leading term (Formula presented) represents the non-zero background; the (Formula presented) term originates from the continuous spectrum; and the (Formula presented) term accounts for the contribution of the pure (Formula presented)-RH problem.