Higher order asymptotics for the Hirota equation via Deift–Zhou higher order theory

•Give RHP for Hirota equation.•Systemically apply Deift–Zhou theory.•Give full asymptotics for Hirota equation.

In this paper, the Deift–Zhou higher order asymptotic theory is used to further establish the full asymptotic expansion for the solution of the Hirota equation to all order, as t→∞t→∞. The method is rigorous and does not rely on an a priori ansatz for the form of the solution.