  We propose the suppression of dispersive spreading of wave packets governed
by the free-space Schr\"odinger equation with a periodically pulsed nonlinear
term. Using asymptotic analysis, we construct stroboscopically-dispersionless
quantum states that are physically reminiscent of, but mathematically different
from, the well-known one-soliton solutions of the nonlinear Schr\"odinger
equation with a constant (time-independent) nonlinearity. Our analytics are
strongly supported by full numerical simulations. The predicted dispersionless
wave packets can move with arbitrary velocity and can be realized in
experiments involving ultracold atomic gases with temporally controlled
interactions.
