The dynamical behaviours 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 Schrödinger (GNLS) equation with local and nonlocal nonlinearities. Using the Vakhitov–Kolokolov criterion, 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 $(R\ll 1)$ to ultrarelativistic $(R\gg 1)$ 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.

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相对论简并激光等离子体中电磁孤子的稳定性和演化

研究了由线性偏振强激光和相对论简并等离子体的非线性相互作用形成的电磁（EM）孤子的动力学行为。在相对论动力学的慢动作近似中，弱非线性电磁包络的演化由具有局部和非局部非线性的广义非线性薛定谔（GNLS）方程描述。使用 Vakhitov-Kolokolov 准则，研究了 GNLS 方程的 EM 孤子解的稳定性。通过孤子速度、孤子特征频率以及简并参数的影响，证明了不同的稳定和不稳定区域 $R=p_{Fe}/m_ec$ ， 在哪里 $p_{Fe}$ 是费米动量和 $m_e$ 电子质量和 $c$ 是真空中的光速。发现稳定区域向不稳定区域转移，随着从弱相对论区域进入而显着减小 $(R\ll 1)$ 到超相对论 $(R\gg 1)$ 电子的简并性。解析预测结果与GNLS方程的模拟结果吻合较好。结果表明，常设 EM 孤子溶液是稳定的。然而，移动的孤子可能是稳定的或不稳定的，这取决于孤子速度、特征频率或简并参数的值。后者具有很强的退化性 $(R>1)$ 最终会导致孤子坍缩。