We show that time variations in the UV ionizing continuum of quasars, on scales of ∼1 year, affect the dynamic structure of the plasmas responsible for low ionization broad absorption lines. Variations of the ionizing continuum produce non-equilibrium photoionization conditions over a significant fraction of the absorbing clouds and supersonically moving ionization fronts. When the flux drops the contraction of the ionized region drives a supersonic cooling front towards the radiation source and a rarefaction wave in the opposite direction. The pressure imbalance is compensated by an increased speed of the cool gas relative to the front. When the flux recovers the cool gas is re-ionized and re-heated by a supersonic ionization front traveling away from the radiation source and a forward shock is created. The reheated clouds equilibrate to a temperature of ∼ 10 4 K and are observed to have different radial velocities than the main cloud. Such fragmentation seems consistent with the multicomponent structure of troughs seen in some objects. The velocity differences measured among various components in the quasars QSO 2359-1241 and SDSS J0318-0600 can be reproduced by our model if strong magnetic fields (∼10 mG) are present within the clouds.