Soliton collisions for a higher-order nonlinear Schrödinger–Maxwell–Bloch system in an erbium-doped fiber

Abstract

Under investigation in this paper is a higher-order nonlinear Schrödinger–Maxwell–Bloch system with quintic terms, which describes the ultrashort optical pulses, up to the attosecond duration, in an erbium-doped fiber. Via the Hirota method and symbolic computation, we derive the one- and two-soliton solutions, while soliton propagation and collision are graphically analyzed: A soliton is shown to maintain its amplitude and shape during the propagation. Soliton collisions are elastic, while bright and dark two solitons are also observed. Head-on collision between the two solitons is illustrated, and shapes of the two solitons do not change during the collision. We discuss the influence of the quadratic, cubic, quartic and quintic coefficients on the collision features: With the value of the quadratic coefficient decreases, widths of the two solitons become larger. Amplitudes of the two solitons decrease with the value of the cubic coefficient reducing. Amplitudes of the two solitons become lower when we reduce the value of the quartic coefficient, and amplitudes of the two solitons decrease with the value of the quintic coefficient decreasing. Overtaking collision between the two solitons can occur, and the two solitons keep their shapes invariant except for the phase shifts before and after the collision. Bound states are also seen between the equal-velocity bright two solitons: They attract and repulse each other periodically. A bound state is formed between the dark two equal-velocity solitons.