Vector solitons for the reduced Maxwell-Bloch equations with variable coefficients in nonlinear optics

Under investigation in this paper is the reduced Maxwell-Bloch equations with variable coefficients, which describe the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric medium. Hirota method and symbolic computation are applied to solve such equations. By introducing the dependent variable transformations, we give the bilinear forms, vector one-, two- and N-soliton solutions in analytic forms. The types of the vector solitons are analyzed: Only the bright-single-hump solitons can be observed in q and r1, the soliton in r2 is the bright-double-hump soliton, and there exist three types of solitons in r3, including the dark-single-hump soliton, dark-double-hump soliton and dark-like-bright soliton, with q as the inhomogeneous electric field, r1 and r2 as the real and imaginary parts of the polarization of the two-level medium, and r3 as the population difference between the ground and excited states. Figures are presented to show the vector soliton solutions. Different types of the interactions between the vector two solitons are presented. In each component, only the overtaking elastic interaction can be observed.