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

9 pages

References in corpus (4)

• Rogue waves of the Hirota and the Maxwell-Bloch equations
• Integrable Motion of Curves in Self-Consistent Potentials : Relation to Spin Systems and Soliton Equations
• On the integrable inhomogeneous Myrzakulov I equation
• Darboux transformation and positons of the inhomogeneous Hirota and the Maxwell-Bloch equation