  We show that both DC and AC Josephson effects with superfluid Fermi atoms in
the BCS-BEC crossover can be described at zero temperature by a nonlinear
Schrodinger equation (NLSE). By comparing our NLSE with mean-field extended BCS
calculations, we find that the NLSE is reliable in the BEC side of the
crossover up to the unitarity limit. The NLSE can be used for weakly-linked
atomic superfluids also in the BCS side of the crossover by taking the
tunneling energy as a phenomenological parameter.
