Exact solutions of the combined HirotaLPD equation with variable coefficients

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 coefficients 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 offering the physi cal descriptions. Analytical treatment to find the nonautonomous rogue waves are investigated for the combined Hirota-LPD equation.