  We explore how wave-particle interactions affect diffusive shock acceleration
(DSA) at astrophysical shocks by performing time-dependent kinetic simulations,
in which phenomenological models for magnetic field amplification (MFA),
Alfvenic drift, thermal leakage injection, Bohm-like diffusion, and a free
escape boundary are implemented. If the injection fraction of cosmic-ray (CR)
particles is greater than 2x10^{-4}, for the shock parameters relevant for
young supernova remnants, DSA is efficient enough to develop a significant
shock precursor due to CR feedback, and magnetic field can be amplified up to a
factor of 20 via CR streaming instability in the upstream region. If scattering
centers drift with Alfven speed in the amplified magnetic field, the CR energy
spectrum can be steepened significantly and the acceleration efficiency is
reduced. Nonlinear DSA with self-consistent MFA and Alfvenic drift predicts
that the postshock CR pressure saturates roughly at 10 % of the shock ram
pressure for strong shocks with a sonic Mach number ranging 20< M_s< 100. Since
the amplified magnetic field follows the flow modification in the precursor,
the low energy end of the particle spectrum is softened much more than the high
energy end. As a result, the concave curvature in the energy spectra does not
disappear entirely even with the help of Alfvenic drift. For shocks with a
moderate Alfven Mach number (M_A<10), the accelerated CR spectrum can become as
steep as E^{-2.1}-E^{-2.3}, which is more consistent with the observed CR
spectrum and gamma-ray photon spectrum of several young supernova remnants.
