  We construct Darboux transformation of a coupled generalized nonlinear
Schr\"odinger (CGNLS) equations and obtain exact analytic expressions of
breather and rogue wave solutions. We also formulate the conditions for
isolating these solutions. We show that the rogue wave solution can be found
only when the four wave mixing parameter becomes real. We also investigate the
modulation instability of the steady state solution of CGNLS system and
demonstrate that it can occur only when the four wave mixing parameter becomes
real. Our results give an evidence for the connection between the occurrence of
rogue wave solution and the modulation instability.
