  The dynamical behaviors of electromagnetic (EM) solitons formed due to
nonlinear interaction of linearly polarized intense laser light and
relativistic degenerate plasmas are studied. In the slow motion approximation
of relativistic dynamics, the evolution of weakly nonlinear EM envelope is
described by the generalized nonlinear Schr{\"o}dinger (GNLS) equation with
local and nonlocal nonlinearities. Using the Vakhitov-Kolokolov criteria, the
stability of an EM soliton solution of the GNLS equation is studied. Different
stable and unstable regions are demonstrated with the effects of soliton
velocity, soliton eigenfrequency, as well as the degeneracy parameter
$R=p_{Fe}/m_ec$, where $p_{Fe}$ is the Fermi momentum and $m_e$ the electron
mass, and $c$ is the speed of light in vacuum. It is found that the stability
region shifts to an unstable one and is significantly reduced as one enters
from the regimes of weakly relativistic $(R\ll1)$ to ultrarelativistic
$(R\gg1)$ degeneracy of electrons. The analytically predicted results are in
good agreement with the simulation results of the GNLS equation. It is shown
that the standing EM soliton solutions are stable. However, the moving solitons
can be stable or unstable depending on the values of soliton velocity, the
eigenfrequency or the degeneracy parameter. The latter with strong degeneracy
$(R>1)$ can eventually lead to soliton collapse.
