In this paper, we study the nonautonomous characteristics of the W-shaped solitons on constant backgrounds for a variable-coefficient higher-order nonlinear Schrodinger (vc-HNLS) equation. Several types of solitons are obtained in exponentially, linearly and periodically fluctuating decreasing dispersion profiles, respectively. We also show the compression effect of the third-order dispersion (TOD) coefficient on the W-shaped soliton. We further analyze the formation and spatiotemporal characteristics of the Peregrine combs (PCs) when TOD coefficient is of the periodic form. Moreover, the PC can be converted into the Peregrine wall if the modulation amplitude is equal to 1.
