Darboux transformation and positons of the inhomogeneous Hirota and the Maxwell-Bloch equation

TL;DR

This paper develops Darboux transformations for the inhomogeneous Hirota and Maxwell-Bloch equations, enabling the derivation of soliton and positon solutions relevant to femtosecond pulse propagation in doped fibers.

Contribution

It introduces a determinant-based Darboux transformation method for the IH-MB equations, providing new explicit solutions for inhomogeneous optical systems.

Findings

Derived soliton solutions for IH-MB equations

Obtained positon solutions demonstrating pulse dynamics

Applicable to femtosecond pulse propagation in doped fibers

Abstract

In this paper, we derive Darboux transformation of the inhomogeneous Hirota and the Maxwell-Bloch(IH-MB) equations which is governed by femtosecond pulse propagation through inhomogeneous doped fibre. The determinant representation of Darboux transformation is used to derive soliton solutions, positon solutions of the IH-MB equations.