Bright-dark soliton solutions and their elastic interaction analysis for a reduced integrable spin Hirota-Maxwell-Bloch equation

Under consideration is a reduced integrable spin Hirota-Maxwell-Bloch (rsHMB) equation, which may have potential applications in describing femtosecond pulse propagation through an erbium doped fiber. With the aid of symbolic computation, we establish the N-fold Darboux transformation (DT) of rsHMB equation based on its known 2 x 2 matrix spectral problem. As an application of the resulting DT, we can get bright-dark soliton and breather solutions of rsHMB equation. Through graphical and asymptotic analysis, the soliton elastic collisions are shown and discussed graphically, and some important soliton physical features including wave velocity, amplitude and energy are analyzed. The consequences and properties presented in this paper may be helpful to comprehend the transmission of optical soliton in erbium doped fiber.