Control and management of the combined Peregrine soliton and Akhmediev breathers in -symmetric coupled waveguides

The coupled nonlinear Schrodinger equation in parity-time-symmetric coupled waveguides with variable coefficients is studied, and exact combined Peregrine soliton and Akhmediev breather solution is derived. Based on this solution, by adjusting the relation between the maximal value and the exciting location value , we discuss the controllable behaviors including the complete excitation, recurrence, maintenance and restraint of the combined Peregrine soliton and Akhmediev breather.