Inverse scattering transform and soliton classification of higher-order nonlinear Schrödinger–Maxwell–Bloch equations

We investigate higher-order nonlinear Schrödinger–Maxwell–Bloch equations using the Riemann–Hilbert method. We perform a spectral analysis of the Lax pair and construct a Riemann–Hilbert problem according to the spectral analysis. As a result, we obtain three types of multisoliton solutions. Based on the analytic solution and with a choice of corresponding parameter values, we obtain solutions of the breather type and a bell-shaped solution and find an interesting phenomenon of the collision of two soliton solutions. We hope that these results can be useful in modeling the wave propagation of a nonlinear optical field in an erbium-doped fiber medium.