  The main purpose of the present paper is to investigate the nonlinear
stability of viscous shock waves and rarefaction wave for bipolar
Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the
micro-macro decomposition to the Boltzmann equation in [21, 23], we first set
up a new micro-macro decomposition around the local Maxwellian related to the
bipolar VPB system and give a unified framework to study the nonlinear
stability of the basic wave patterns to the system. Then, as the applications
of this new decomposition, the time-asymptotic stability of the two typical
nonlinear wave patterns, viscous shock waves and rarefaction wave, are proved
for the 1D bipolar Vlasov-Poisson-Boltzmann system. More precisely, it is first
proved that the linear superposition of two Boltzmann shock profiles in the
first and third characteristic fields is nonlinearly stable to the 1D bipolar
VPB system up to some suitable shifts without the zero macroscopic mass
conditions on the initial perturbations. Then the time-asymptotic stability of
rarefaction wave fan to compressible Euler equations is proved to 1D bipolar
VPB system. These two results are concerned with the nonlinear stability of
wave patterns for Boltzmann equation coupled with additional (electric) forces,
which together with spectral analysis made in [18] sheds light on understanding
the complicated dynamic behaviors around the wave patterns in the
transportation of charged particles under the binary collisions, mutual
interactions, and the effect of the electrostatic potential forces.
