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In this Letter, we show that a three-dimensional Bose-Einstein solitary wavecan become stable if the dispersion law is changed from quadratic to quartic.We suggest a way to realize the quartic dispersion, using shaken opticallattices. Estimates show that the resulting solitary waves can occupy as littleas $\sim 1/20$-th of the Brillouin zone in each of the three directions andcontain as many as $N = 10^{3}$ atoms, thus representing a \textit{fullymobile} macroscopic three-dimensional object.

Three-dimensional Gross-Pitaevskii solitary waves in optical lattices:  stabilization using the artificial quartic kinetic energy induced by lattice  shaking