  In this paper, we construct a generalized Darboux transformation to the
coupled Hirota equations with high-order nonlinear effects like the third
dispersion, self-steepening and inelastic Raman scattering terms. As
application, an Nth-order localized wave solution on the plane backgrounds with
the same spectral parameter is derived through the direct iterative rule. In
particular, some semi-rational, multi-parametric localized wave solutions are
obtained: (1) Vector generalization of the first- and the second-order rogue
wave solution; (2) Interactional solutions between a dark-bright soliton and a
rogue wave, two dark-bright solitons and a second-order rogue wave; (3)
Interactional solutions between a breather and a rogue wave, two breathers and
a second-order rogue wave. The results further reveal the striking dynamic
structures of localized waves in complex coupled systems.
