Darboux transformations and solutions of nonlocal Hirota and Maxwell-Bloch equations

In this paper, based on the Hirota and Maxwell-Bloch (H-MB) system and its application in the theory of the femtosecond pulse propagation through an erbium doped fiber, we define two kinds of nonlocal Hirota and Maxwell-Bloch (NH-MB) systems, namely, PT-symmetric NH-MB system and reverse space-time NH-MB system. Then, we construct the Darboux transformations of these NH-MB systems. Meanwhile, we derive the explicit solutions by the Darboux transformations.

Automated summary

This paper introduces two new types of nonlocal Hirota and Maxwell-Bloch (NH-MB) systems, namely, the PT-symmetric NH-MB system and the reverse space-time NH-MB system, based on the original H-MB system. Darboux transformations were then constructed for these NH-MB systems, leading to explicit solutions being derived.