Solitons in PT symmetric Manakov system

Parity-time (PT)-symmetric Manakov system including four cases are discussed in this paper, which is used to depict the nonlinear waves in optical fibers. Via constructing the generalized Manakov system, soliton/soliton-like solutions of PT-symmetric Manakov system are attained: First and second cases are the solitons and periodic solutions, respectively; Third and fourth cases are the soliton-like solutions. Loss and gain of the soliton-like propagation is not balanced in the third and fourth cases, which is consistent with the experimental result. Time frequency-spectrum of the fourth case are analyzed: Phase spectrum of the one-order soliton-like and amplitude spectrum of the two-order soliton-like both have periodic perturbation. Besides, bilinear forms of the M(M > 2)-coupled PT-symmetric Manakov system are also attained, which can help us to obtain the M-dimension vector solitons and discuss the nonlinear waves in multi-mode optical fibers. At the end of this paper, we display the rogue waves of generalized Manakov system and discuss the relations between the linear turbulence and rogue-wave's shape. Amplitude of the rogue wave is increased with a phase-shift parameter (delta 1). Time frequency-spectrum of the rogue wave are analyzed.