We employ the Riemann–Hilbert (RH) method to investigate the multiple higher-order pole solutions of the integrable coupled Hirota equations characterized by a \(3\times 3\) Lax pair. Using the direct scattering transform, we investigate the analyticity and symmetry of the Jost solutions and the scattering matrix, with a particular focus on the discrete spectrum problem associated with multiple higher-order poles. The inverse scattering problem is addressed through a corresponding \(3\times 3\) matrix-valued RH problem that relates to the residual conditions of these higher-order poles. We derive the reconstruction formula for the solution. Then, under reflectionless conditions, we successfully resolve the RH problem, transforming it into a linear algebraic system, and obtain the formula for solutions with multiple higher-order poles to the coupled Hirota equations. Finally, we present the dynamical behaviors of various multiple higher-order pole solutions and their interactions. These findings will prove instrumental in elucidating various nonlinear wave phenomena and can be effectively utilized across a range of physical contexts.
