In this paper, we construct exact families of traveling wave (periodic wave, singular wave, singular-periodic wave, singular-solitary wave and shock wave) solutions of a well-known equation of nonlinear PDE, the variable COE, cients combined Hirota-Lakshmanan-Porsezian-Daniel (Hirota-LPD) equation with the fourth nonlinearity, which describes an important development, and application of soliton dispersion management experiment in nonlinear optics is considered, and as an achievement, a series of exact traveling wave solutions for the aforementioned equation is formally extracted. This nonlinear equation is solved by using the extended trial equation method (ETEM) and the improved tan(ϕ, =2)-expansion method (ITEM). Meanwhile, the mechanical features of some families are explained through o , ering the physi-cal descriptions. Analytical treatment to , nd the nonautonomous rogue waves are investigated for the combined Hirota-LPD equation.