Chaos in the dynamics of electromagnetic solitons in relativistic degenerate plasmas

We propose a coupled system for the nonlinear interaction between high-frequency, circularly polarized, intense electromagnetic (EM) waves and low-frequency electron-density perturbations, driven by the EM-wave ponderomotive force, in an unmagnetized plasma composed of fully degenerate relativistic electrons and stationary positive ions, including a higher-order correction to the nonlocal nonlinearity. We show that the modulational instability growth rate associated with the generation of EM envelope solitons is significantly reduced with a slight increase in either the nonlocal nonlinear correction or the degeneracy parameter. Furthermore, a three-wave temporal model predicts the existence of quasiperiodic and chaotic states of EM solitons while interacting with longitudinal electron-density perturbations. We show that the greater the degeneracy (or higher the contribution from the nonlocal correction), the smaller the instability domain of modulation wave numbers; thus, degeneracy favors the stability of EM soliton evolution. The existence of temporal chaos in a low-dimensional model could be a signature of the development of spatiotemporal chaos in the complete nonlinear model, in which many electromagnetic solitons can be excited and saturated as they interact with electron plasma waves.