  We present variational and numerical solutions of the generalized
Gross--Pitaevskii equation for an atomic Bose--Einstein condensate with
time-dependent, laser-induced dipole-dipole interactions (LIDDI). The formation
of a supersolid ground state due to LIDDI in an elongated (cigar-shaped) BEC is
investigated. It is found that the supersolid structure emerges if the laser
intensity exceeds a critical value, which depends on the linear density of
atoms in the BEC.
