Exotic dynamics of breather and rogue waves in a coupled nonlinear Schrödinger equation

Under investigation in this work is a coupled nonlinear Schrödinger equation (CNLSE), which can be used to describe the dynamics of light beams and pulses in [Formula: see text]-symmetric coupled waveguides. Its breather wave (BW) and rogue wave (RW) solutions are presented here. The BW solutions can be converted into various soliton solutions including the Akhmediev breather, Kuznetsov–Ma soliton breather and Peregrine soliton. The dynamics of the solutions are graphically discussed. Moreover, we observe that the two BWs can evolve into an Akhmediev breather with a Peregrine soliton. We hope that the results can be used to enrich dynamical behavior of BWs and rogue waves in the CNLSE.