  Background: Heavy-ion fusion reactions at energies near the Coulomb barrier
are influenced by couplings between the relative motion and nuclear intrinsic
degrees of freedom of the colliding nuclei. The time-dependent Hartree-Fock
(TDHF) theory, incorporating the couplings at the mean-field level, as well as
the coupled-channels (CC) method are standard approaches to describe low energy
nuclear reactions.
  Purpose: To investigate the effect of couplings to inelastic and transfer
channels on the fusion cross sections for the reactions $^{40}$Ca+$^{58}$Ni and
$^{40}$Ca+$^{64}$Ni.
  Methods: Fusion cross sections around and below the Coulomb barrier have been
obtained from coupled-channels (CC) calculations, using the bare
nucleus-nucleus potential calculated with the frozen Hartree-Fock method and
coupling parameters taken from known nuclear structure data. The fusion
thresholds and neutron transfer probabilities have been calculated with the
TDHF method.
  Results: For $^{40}$Ca+$^{58}$Ni, the TDHF fusion threshold is in agreement
with the most probable barrier obtained in the CC calculations including the
couplings to the low-lying octupole $3_1^{-}$ state for $^{40}$Ca and to the
low-lying quadrupole $2_1^{+}$ state for $^{58}$Ni. This indicates that the
octupole and quadrupole states are the dominant excitations while neutron
transfer is shown to be weak. For $^{40}$Ca+$^{64}$Ni, the TDHF barrier is
lower than predicted by the CC calculations including the same inelastic
couplings as those for $^{40}$Ca+$^{58}$Ni. TDHF calculations show large
neutron transfer probabilities in $^{40}$Ca+$^{64}$Ni which could result in a
lowering of the fusion threshold.
  Conclusions: Inelastic channels play an important role in $^{40}$Ca+$^{58}$Ni
and $^{40}$Ca+$^{64}$Ni reactions. The role of neutron transfer channels has
been highlighted in $^{40}$Ca+$^{64}$Ni.
