Painlevé-type asymptotics for the defocusing Hirota equation in transition region

We consider the long-time asymptotics for defocusing Hirota equation with Schwartz Cauchy data in transition region. On basis of direct and inverse scattering transform Lax pair equations, we first express solution problem terms a Riemann–Hilbert problem. Further, apply nonlinear steepest descent analysis to obtain critical region | x / t − stretchy="false">( α 2 3 β stretchy="false">) ≤ M , where is positive constant. Our result shows that can be expressed Painlevé II equation.