High-density low-temperature plasmas with degenerate species are considered in the limit of high Fermi velocities close to the speed of light. The small amplitude ion-acoustic solitons are studied in this regime. The analysis presented here is based on a relativistic hydrodynamic model with the average reverse gamma factor evolution consisting of the equations for the evolution of the functions such as the concentration, the velocity field, the average reverse relativistic gamma factor, and the flux of the reverse relativistic gamma factor, which are considered as main hydrodynamic variables. Justification of the suggested model via comparison of the hydrodynamic results with the result of application of the relativistic Vlasov kinetic equation is made in the linear approximation.
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