Inhomogeneous reduced Maxwell-Bloch system in nonlinear optics: Darboux-transformation and solitonic issues

Abstract

Studies on nonlinear optics are active, providing the applications in modulators, fiber lasers, optical sensors, etc. In this paper, we investigate an inhomogeneous reduced Maxwell-Bloch system, which could describe the ultra-short optical pulses through an inhomogeneous medium. N-fold Darboux transformation is constructed via an existing Lax pair, where N is a positive integer. Generalized Darboux transformation is obtained via a limit procedure. One- and two-soliton solutions are determined with the aid of the N-fold Darboux transformation. Double-pole soliton solutions are derived via the generalized Darboux transformation. With respect to the electric field, microscopic polarization, phase information, and atomic inversion related to the inhomogeneous medium, one soliton, interaction between the two solitons, and double-pole soliton are graphically depicted. Effects of the coefficients in that system on those solitons are shown via the trigonometric and linear functions.