LAUSR

Abstract In this paper, the variable coefficients coupled Hirota equation is investigated by virtue of the unified method. Playing an important role in optics, the coupled Hirota equation describes the transmission process when high intensity ultra-short pulses pass through an optical glass fiber. Two types of complex wave solutions, polynomial function and rational function solutions, are gained. The polynomial function solutions incorporate complex solitary, complex soliton and complex elliptic wave solutions, while the rational function solutions involve complex periodic and complex soliton wave solutions. Furthermore, by choosing different values of the parameters, we illustrate the dynamical behaviors and the physical signification of these solutions.