  We explore nonlinear effects of wave-particle interactions on the diffusive
shock acceleration (DSA) process in Type Ia-like, SNR blast waves, by
implementing phenomenological models for magnetic field amplification,
Alfv'enic drift, and particle escape in time-dependent numerical simulations of
nonlinear DSA. For typical SNR parameters the CR protons can be accelerated to
PeV energies only if the region of amplified field ahead of the shock is
extensive enough to contain the diffusion lengths of the particles of interest.
Even with the help of Alfv'enic drift, it remains somewhat challenging to
construct a nonlinear DSA model for SNRs in which order of 10 % of the
supernova explosion energy is converted to the CR energy and the magnetic field
is amplified by a factor of 10 or so in the shock precursor, while, at the same
time, the energy spectrum of PeV protons is steeper than E^{-2}. To explore the
influence of these physical effects on observed SNR emissions, we also compute
resulting radio-to-gamma-ray spectra. Nonthermal emission spectra, especially
in X-ray and gamma-ray bands,depend on the time dependent evolution of CR
injection process, magnetic field amplification, and particle escape, as well
as the shock dynamic evolution. This result comes from the fact that the high
energy end of the CR spectrum is composed of the particles that are injected in
the very early stages of blast wave evolution. Thus it is crucial to understand
better the plasma wave-particle interactions associated with collisionless
shocks in detail modeling of nonthermal radiation from SNRs.
