  We theoretically study the stability of a trapless dipolar Bose-Einstein
condensate (BEC) with temporal modulation of short-range contact interaction.
For this aim, through both analytical and numerical methods, we solve a
Gross-Pitaevskii equation with both constant and oscillatory form of
short-range contact interaction along with long-range, nonlocal, dipole-dipole
(DD) interaction terms. Using variational method, we discuss the stability of
the trapless dipolar BEC with presence and absence of both constant and
oscillatory contact interactions. We show that the oscillatory contact
interaction prevents the collapse of the trapless dipolar BEC. We confirm the
analytical prediction through numerical simulations. We have also studied the
collective excitations in the system induced by the effective potential due to
oscillating interaction.
