Explicit solutions of nonlocal reverse-time Hirota-Maxwell-Bloch system

In this paper, we investigate the nonlocal reverse-time Hirota-Maxwell-Bloch system, focusing on its soliton solutions using the Darboux transformation method. By deriving the Darboux transformation for this system, we obtained explicit expressions for the new potentials $q^{\prime },p^{\prime }$, and ${\eta }^{\prime }$ in both the defocusing ( $\kappa =1$) and focusing ( $\kappa =-1$) cases. Our analysis reveals significant differences in soliton behavior depending on the value of $\kappa$, with the defocusing case producing wide, smooth solitons and the focusing case yielding narrow, highly localized solitons. These results provide a deeper understanding of soliton dynamics in nonlocal integrable systems and lay the groundwork for future studies on the influence of nonlocality in integrable models.