Solitons for the (2+1)-dimensional nonlinear Schrödinger-Maxwell-Bloch equations in an erbium-doped fibre. Issue 6 (25th March 2016) - Wu, Xiao-Yu; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong; Sun, Ya
Abstract : Under investigation in this paper is a set of the ( 2 + 1 ) -dimensional nonlinear Schrödinger–Maxwell–Bloch (NLS–MB) equations, which describes the optical pulse propagation in an erbium-doped fibre. Employing the Hirota method and symbolic computation, we obtain the one- two- and N-soliton solutions. We prove that the interactions between the two solitons are elastic through the asymptotic analysis on the soliton solutions. Figures are plotted to show the one soliton and the interaction between the two solitons. We find that the decrease of the frequency shift from the resonance can make the angle between the propagation directions and the amplitudes of the two MB solitons bigger, implying that the change of the amplitudes of the two MB solitons is closely related to the propagation directions of the two NLS solitons.