Vector semirational rogue waves for a coupled nonlinear Schrödinger system in a birefringent fiber

Under investigation in this paper is a coupled nonlinear Schrödinger system with the four-wave mixing term, which describes the propagation of optical waves in a birefringent fiber. Via the Darboux dressing transformation, the semirational solutions which give rise to the vector rogue waves and breathers are obtained. We display the vector rogue waves and the interaction between the rogue waves and bright-dark solitons. During the interaction, breather-like structures arise because of the interference between the dark and bright components of the soliton. Besides, it can be observed that the rogue wave and soliton merge together. Interactions between the breathers and bright-dark solitons are shown graphically. Keeping |α1|2a+|α2|2c+bα1α2∗+b∗α1∗α2 invariant, we find that the smaller value of ac−|b|2 yields the more obvious breather-like structure, with a and c representing the self- and cross-phase modulations, respectively, b representing the four-wave mixing effect, α1 and α2 being two constants. Similarly, keeping ac−|b|2 invariant, we find that the smaller value of |α1|2a+|α2|2c+bα1α2∗+b∗α1∗α2 yields the more obvious breather-like structure. Bound state forming between the Kuznetsov-Ma soliton and breather-like structure is illustrated.