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We develop a model of early X-ray afterglows of gamma-ray bursts originatingfrom the reverse shock (RS) propagating through ultra-relativistic, highlymagnetized pulsar-like winds produced by long-lasting central engines. We firstperform fluid and MHD numerical simulations of relativistic double explosions.We demonstrate that even for constant properties of the wind a variety oftemporal behaviors can be produced, depending on the energy of the initialexplosion and the wind power, the delay time for the switch-on of the wind, andmagnetization of the wind. X-ray emission of the highly magnetized RS occurs inthe fast cooling regime - this ensures high radiative efficiency and allowsfast intensity variations. We demonstrate that: (i) RS emission naturallyproduces light curves showing power-law temporal evolution with varioustemporal indices; (ii) mild wind power, of the order of $\sim 10^{46}$ ergs$^{-1}$ (equivalent isotropic), can reproduce the afterglows' plateau phase;(iii) termination of the wind can produce sudden steep decays; (iv)short-duration afterglow flares are due to mild variations in the windluminosity, with small total injected energy.

Dynamics and emission of wind-powered afterglows of gamma-ray bursts: flares, plateaus and steep decays