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

TL;DR

This paper introduces nonlocal versions of the Hirota and Maxwell-Bloch systems, constructs Darboux transformations for them, and derives explicit solutions, advancing the understanding of nonlocal integrable systems in fiber optics.

Contribution

It defines two types of nonlocal Hirota-Maxwell-Bloch systems, constructs their Darboux transformations, and obtains explicit solutions, which is a novel extension in the study of nonlocal integrable equations.

Findings

Defined PT-symmetric and reverse space-time nonlocal systems

Constructed Darboux transformations for these systems

Derived explicit solutions using the transformations

Abstract

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.