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

Stability and evolution of electromagnetic solitons in relativistic degenerate laser plasmas