We consider the Vlasov--Poisson system describing a two-species plasma with
spatial dimension 1 and the velocity variable in Rn. We find the
necessary and sufficient conditions for the existence of solitary waves, shock
waves, and wave trains of the system, respectively. To this end, we need to
investigate the distribution of ions trapped by the electrostatic potential.
Furthermore, we classify completely in all possible cases whether or not the
traveling wave is unique. The uniqueness varies according to each traveling
wave when we exclude the variant caused by translation. For the solitary wave,
there are both cases that it is unique and nonunique. The shock wave is always
unique. No wave train is unique.Comment: 56 pages, 9 figure