  A number of possible pulsar radio emission mechanisms are based on streaming
instabilities in relativistically hot electron-positron pair plasmas. At
saturation the unstable waves can form, in principle, stable solitary waves
which could emit the observed intense radio signals. We searched for the proper
plasma parameters which would lead to the formation of solitons, investigated
their properties and dynamics as well as the resulting oscillations of
electrons and positrons possibly leading to radio wave emission. We utilized a
one-dimensional version of the relativistic Particle-in-Cell code ACRONYM
initialized with an appropriately parameterized one-dimensional
Maxwell-J\"uttner velocity space particle distribution to study the evolution
of the resulting streaming instability in a pulsar pair plasma. We found that
strong electrostatic superluminal L-mode solitons are formed for plasmas with
normalized inverse temperatures $\rho \geq 1.66$ or relative beam drift speeds
with Lorentz factors $\gamma > 40$. The parameters of the solitons fulfill the
wave emission conditions. For appropriate pulsar parameters the resulting
energy densities of superluminal solitons can reach up to $1.1 \times 10^5$
erg$\cdot$cm$^{-3}$, while those of subluminal solitons reach only up to $1.2
\times 10^4$ erg$\cdot$cm$^{-3}$. Estimated energy densities of up to $7 \times
10^{12}$ erg$\cdot$cm$^{-3}$ suffice to explain pulsar nanoshots.
