Abstract
The first- and second-order localized waves for a variable-coefficient coupled Hirota equation describe the vector optical pulses in inhomogeneous optical fiber and are investigated via generalized Darboux transformation in this work. Based on the equation’s Lax pair and seed solutions, the localized wave solutions are calculated, and the dynamics of the obtained localized waves are shown and analyzed through numerical simulation. A series of novel dynamical evolution plots illustrating the interaction between the rogue waves and dark-bright solitons or breathers are provided. It is found that functions have an influence on the propagation of shape, period, and velocity of the localized waves. The presented results contribute to enriching the dynamics of localized waves in inhomogeneous optical fiber.