Ion-acoustic solitons in a relativistic Fermi plasma at finite temperature

The theory of ion-acoustic solitons in nonrelativistic fully degenerate plasmas and nonrelativistic and ultra-relativistic degenerate plasmas at low temperatures is known. We consider a multi-component relativistic degenerate electron-positron-ion plasma at finite temperatures. Specifically, we focus on the intermediate region where the particle's thermal energy $$ and the rest mass energy $$ do not differ significantly, i.e., $$ . However, the Fermi energy $$ is larger than the thermal energy and the normalized chemical energy ( $$ ) is positive and finite. Two different parameter regimes with $$ and $$ , relevant for astrophysical plasmas, are defined, and the existence of small amplitude ion-acoustic solitons in these regimes are studied, including the critical cases where the known KdV (Korteweg-de Vries) theory fails. We show that while the solitons with both the positive (compressive) and negative (rarefactive) potentials coexist in the case of $$ , only compressive solitons can exist in the other regime $$ . Furthermore, while the rarefactive solitons within the parameter domains of $$ and $$ can evolve with increasing amplitude and hence increasing energy, the energy of compressive solitons reaches a steady state.