Abstract
An enthalpy function Hj∝1+ηj2 is deduced from the density of states for degenerate relativistic charged particulate. Here ηj=pj/mjc2 stands for the relativistic factor, pjmj is the Fermi momentum (mass) for the jth degenerate relativistic species and c designates the vacuum speed of light. The enthalpy function reduces the results Weinberg (1972), Lee and Cheong (2007) obtained for the nondegenerate nonrelativistic (NR) and ultrarelativistic (UR) fluids. The linear and nonlinear propagation characteristics of the electron-acoustic (EA) solitons are examined for dense electron–positron–ion (EPI) plasma that comprises degenerate relativistic electrons/positrons and non-degenerate ions. By using Hj and with the aid of the relativistic hydrodynamic equations, a linear dispersion relation for the EA waves is derived that admits the evolution of the fast and slow electron-acoustic (FEA/SEA) excitations. For the nonlinear EA waves, a Korteweg–de Vries (KdV) equation is obtained; numerical analysis reveals that the FEA mode may ensue in the solitary potential. The propagation of the SEA solitons is forbidden as it suffers from a negative phase dispersion effect. At a relatively low concentration of positrons, the EPI plasma may admit the evolution of electron–holes and therefore, give rise to the compressive FEA solitons. This investigation is important for understanding localized excitations in degenerate relativistic plasmas, as that are relevant in white dwarfs, neutron stars, and high-energy density facilities.
•An enthalpy function is deduced from density of states for degenerate relativistic charged particulate.•The propagation characteristics of EA solitons are examined in a degenerate relativistic EPI plasma.•A linear dispersion relation for the fast/slow FEA/SEA excitations EA waves is derived.•For the nonlinear EA waves, a KdV equation is obtained.•The numerical analysis reveals that the FEA mode may excite the solitary potentials.