  Coherent radiation of pulsars, magnetars, and fast radio bursts could, in
theory, be interpreted as radiation from solitons and soliton-like waves. The
solitons are meant to contain a large number of electric charges confined on
long time-scales and may radiate strongly by coherent curvature emission.
However, solitons are also known to undergo a wave collapse, which may cast
doubts on the correctness of the soliton radio emission models of neutron
stars.
  We investigate the evolution of the caviton type of solitons
self-consistently formed by the relativistic streaming instability and compare
their apparent stability in 1D calculations with more generic 2D cases, in
which the solitons are seen to collapse. Three representative cases of beam
Lorentz factors and plasma temperatures are studied to obtain soliton
dispersion properties. We utilized 1D electrostatic and 2D electromagnetic
relativistic particle-in-cell simulations at kinetic microscales.
  We found that no solitons are generated by the streaming instability in the
2D simulations. Only superluminal L-mode (relativistic Langmuir) waves are
produced during the saturation of the instability, but these waves have smaller
amplitudes than the waves in the 1D simulations. The amplitudes tend to
decrease after the instability has saturated, and only waves close to the light
line, $\omega = c k$, remain. Solitons in the 1D approach are stable for
$\gamma_\mathrm{b} \gtrsim 60$, but they disappear for low beam Lorentz factor
$\gamma_\mathrm{b} < 6$.
  Our examples show that the superluminal soliton branch that is formed in 1D
simulations will not be generated by the relativistic streaming instability
when more dimensional degrees of freedom are present - unless one can show that
there are alternative plasma mechanisms for the soliton generation.
