  We study a problem of non-adiabatic superfluid dynamics of spin-orbit coupled
neutral fermions in two spatial dimensions. We focus on the two cases when the
out-of-equilibrium conditions are initiated either by a sudden change of the
pairing strength or the population imbalance. For the case of zero population
imbalance and within the mean-field approximation, the non-adiabatic evolution
of the pairing amplitude in a collisionless regime can be found exactly by
employing the method of Lax vector construction. Our main finding is that the
presence of the spin-orbit coupling significantly reduces the region in the
parameter space where a steady state with periodically oscillating pairing
amplitude is realized. For the collisionless dynamics initiated by a sudden
disappearance of the population imbalance we obtain an exact expression for the
steady state pairing amplitude. In the general case of quenches to a state with
finite population imbalance we show that there is a region in the steady state
phase diagram where at long times the pairing amplitude dynamics is governed by
the reduced number of the equations of motion in full analogy with exactly
integrable case.
