Long-time asymptotics for the initial-boundary value problem of coupled Hirota equation on the half-line

Abstract

The object of this work is to investigate the initial-boundary value problem for coupled Hirota equation on the half-line. We show that the solution of the coupled Hirota equation can be expressed in terms of the solution of a 3 × 3 matrix Riemann-Hilbert problem formulated in the complex k-plane. The relevant jump matrices are explicitly given in terms of the matrix-valued spectral functions s(k) and S(k) that depend on the initial data and boundary values, respectively. Then, applying nonlinear steepest descent techniques to the associated 3 × 3 matrix-valued Riemann-Hilbert problem, we can give the precise leading-order asymptotic formulas and uniform error estimates for the solution of the coupled Hirota equation.