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

Generalized Darboux transformation and localized waves in coupled Hirota equations