  We derive generalized nonlinear wave solution formula for mixed coupled
nonlinear Sch\"odinger equations (mCNLSE) by performing the unified Darboux
transformation. We give the classification of the general soliton formula on
the nonzero background based on the dynamical behavior. Especially, the
conditions for breather, dark soliton and rogue wave solution for mCNLSE are
given in detail. Moreover, we analysis the interaction between dark-dark
soliton solution and breather solution. These results would be helpful for
nonlinear localized wave excitations and applications in vector nonlinear
systems.
