Darboux tranformation and solutions of the (2+1)-dimensional Schrödinger-Maxwell-Bloch equation

Abstract

In this paper, we construct a Darboux transformation (DT) of the (2+1)-dimensional Schrödinger-Maxwell-Bloch equation (SMBE) which is integrable by the Inverse Scattering Method. Using this DT, the one-soliton solution and periodic solution are obtained from the "seed" solutions.

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

“…where m ′ 11 = m 11 | ǫ1=1,ǫ2=0 and m ′ 12 = m 12 | ǫ1=1,ǫ2=0 . This solution was obtained in [6]. b) Now let we put ǫ 1 = 0, ǫ 2 = 1.…”