Long-time asymptotics of solution to the coupled Hirota system with 4 × 4 Lax pair

Abstract

We study the Cauchy problem for the integrable coupled Hirota system with a 4×4 Lax pair on the line with decaying initial data. By deriving a Riemann–Hilbert representation for the solution, we compute the precise leading-order terms for long-time asymptotics based on the nonlinear steepest descent arguments.