  We construct dark-dark solitons, general breather (GB), Akhmediev breather
(AB), Ma soliton (MS) and rogue wave (RW) solutions of a coupled generalized
nonlinear Schr\"odinger (CGNLS) equation. While the dark-dark solitons are
captured in the defocusing regime of CGNLS system, the other solutions, namely
GB, AB, MS and RW, are identified in the focusing regime. We also analyze the
structures of GB, AB, MS and RW profiles with respect to the four-wave mixing
parameter. We show that when we increase the value of the real part of the four
wave mixing parameter, the number of peaks in the breather profile increases
and the width of each peak gets shrunk. Interestingly the direction of this
profile also changes due to this change. As far as the RW profile is concerned
the width of the peak becomes very thin when we increase the value of this
parameter. Further, we consider RW solution as the starting point and derive
AB, MS and GB in the reverse direction and show that the solutions obtained in
both the directions match with each other. In the course of the reverse
analysis we also demonstrate how to capture the RW solutions directly from AB
and MS.
