The <i>N</i>-soliton solutions of the three-component coupled nonlinear Hirota equations based on Riemann–Hilbert method

Abstract In order to more accurately and effectively consider the propagation process of solitons in electromagnetic pulse waves and make full use of wavelength division multiplexing, we study a class of high-order three-component Hirota equations by the Riemann–Hilbert method. Under zero boundary conditions and given initial conditions q j ( x ,0), the N -soliton solutions of the equations are obtained by constructing and solving Riemann–Hilbert problems based on matrix spectral problem. Specifically, we discuss the cases of N = 1, 2, analyze the dynamical properties of 1-soliton and 2-soliton solutions through numerical simulations, and summarize the effect of integrable perturbations and spectral parameters on soliton motion.