  We find that diverse nonlinear waves, such as soliton, Akhmediev breather,
and rogue waves (RWs), can emerge and interplay with each other in a two-mode
coupled system. It provides a good platform to study interaction between
different kinds of nonlinear waves. In particular, we obtain dark RWs
analytically for the first time in the coupled system, and find that two RWs
can appear in the temporal-spatial distribution. Possible ways to observe these
nonlinear waves are discussed.
