Darboux transformation and vector solitons for a variable-coefficient coherently coupled nonlinear Schrodinger system in nonlinear optics

Efforts have been put into investigating a variable-coefficient coherently coupled nonlinear Schrodinger system with the alternate signs of nonlinearities, describing the propagation of the waves in the nonlinear birefringent optical fiber. Via the Lax pair, Darboux transformation for the system is derived. Then, we derive the vector one-and two-soliton solutions. Figures are displayed to help us study the properties of the vector solitons: with the strength of the four-wave mixing terms gamma(t) as a constant, the vector soliton propagates with the unvarying velocity and amplitude; with gamma(t) being a time-dependent function, amplitude and velocity of the vector soliton keep varying during the propagation; bell-and M-shaped solitons can both be observed in q(2) mode, while we just observe the bell-shaped soliton in q(1) mode, where q(1) and q(2) are the two slowly varying envelopes of the propagating waves; head-on and overtaking interactions between the vector two solitons are both presented. (C) 2016 Society of Photo-Optical Instrumentation Engineers (SPIE)