The (2+1)-dimensional Hirota-Maxwell-Bloch equation: Darboux transformation and soliton solutions

TL;DR

This paper develops a Darboux transformation for the integrable (2+1)-dimensional Hirota-Maxwell-Bloch equation and derives explicit one- and multi-soliton solutions.

Contribution

It introduces a Darboux transformation for the (2+1)-dimensional HMBE and constructs explicit soliton solutions, advancing solution methods for this integrable system.

Findings

Constructed Darboux transformation for the HMBE

Derived explicit one-soliton solution

Presented general form of n-soliton solutions

Abstract

The (2+1)-dimensional Hirota-Maxwell-Bloch equation (HMBE) is integrable by the Inverse Scattering Method. In this paper, we construct a Darboux transformation (DT) of the (2+1)-dimensional HMBE. Also the one-soliton solution obtained by means of the one-fold DT. For the $n$-soliton solution the general form is presented.