  Using time-dependent Ginzburg-Landau theory, we study the role of amplitude
and phase fluctuations in the recovery of charge and spin stripe phases in
response to a pump pulse that melts the orders. For parameters relevant to the
case where charge order precedes spin order thermodynamically, amplitude
recovery governs the initial time scales, while phase recovery controls
behavior at longer times. In addition to these intrinsic effects, there is a
longer spin re-orientation time scale related to the scattering geometry that
dominates the recovery of the spin phase. Coupling between the charge and spin
orders locks the amplitude and similarly the phase recovery, reducing the
number of distinct time scales. Our results well reproduce the major
experimental features of pump-probe x-ray diffraction measurements on the
striped nickelate La$_{1.75}$Sr$_{0.25}$NiO$_4$. They highlight the main idea
of this work, which is the use of time-dependent Ginzburg-Landau theory to
study systems with multiple coexisting order parameters.
