Long-time asymptotic for the Hirota equation via nonlinear steepest descent method

We present the Riemann–Hilbert problem formalism for the initial value problem for the Hirota equation on the line. We show that the solution of this initial value problem can be obtained from that of associated Riemann–Hilbert problem, which allows us to use nonlinear steepest descent method/Deift–Zhou method to analyze the long-time asymptotic for the Hirota equation.