Soliton excitation in a weak relativistic quantum plasma

Abstract

In a weakly relativistic plasma, the influence of quantum mechanics becomes evident through a finite Fermi temperature despite moderately high particle velocities, indicating a degenerate electron gas with significant quantum pressure. The plasma’s inherent nonlinearity allows for forming and propagating solitons, which are self-localized wave packets. The quantum considerations modify solitons’ dispersion and stability compared to a purely classical plasma. However, the ideal picture is often challenged by various interactions that can be incorporated into such a plasma. The effects of exchange, viscosity, and collision, as some inevitable interactions, are studied here to provide a more realistic picture of the soliton excitations in the plasma. The model’s analytical solutions are obtained through the Tanh approach in a perturbation manner. This approach is adopted considering the theory’s nonlinearity and is different from the conventional perturbation methods of linearization. The results show that viscosity and collision or dissipation are correlated and interdependent, so the viscosity coupling constant is four times the dissipation coupling constant. Also, the viscosity and dissipation have diminished effects and reduce the amplitude of the vector potential, while the exchange considerations have intensifying consequences.