Localized wave solutions to a variable-coefficient coupled Hirota equation in inhomogeneous optical fiber

Abstract Higher-order localized waves for a variable-coefficient coupled Hirota equation describes the vector optical pulses in inhomogeneous optical fiber and are investigated via generalized Darboux transformation in this work. Based on its Lax pair and seed solutions, the localized wave solutions are calculated, evolution plots are constructed, and the dynamics of the obtained localized waves are analyzed through numerical simulation. It is observed that the first- and second-order localized waves interact with dark-bright solitons or breathers, and the functions α(t), β(t), and δ(t) determine the propagation shape of the localized waves. The presented results contribute to enriching the dynamics of localized waves in inhomogeneous optical fiber. Keywords: variable-coefficient coupled Hirota equation; generalized Darboux transformation; soliton; breather