Analytical traveling-wave and solitary solutions to the generalized Gross-Pitaevskii equation with sinusoidal time-varying diffraction and potential

We determine analytical extended traveling-wave and spatiotemporal solitary solutions to the generalized (3+1)-dimensional Gross-Pitaevskii equation with time-dependent coefficients, for the sinusoidally time-varying diffraction and quadratic potential strength. A number of periodic and localized solutions are obtained whose intensity does not decrease in time in the absence of externally induced gain or loss. Stability analysis of our solitary solutions is carried out, to display their modulational stability.