Multi-rogue wave and multi-breather solutions in -symmetric coupled waveguides

The coupled nonlinear Schrödinger equation in parity-time symmetric coupled waveguides is studied by means of the modified Darboux transformation method. The hierarchies of rational solutions and breather solutions are generated from the plane wave solution. Some basic properties of multi-rogue waves and multi-breathers including the superposed Kuznetsov–Ma solitons, Akhmediev breathers and their combined structures are discussed. Our results might provide useful information for potential applications of synthetic parity-time symmetric systems in nonlinear optics and condensed matter physics.