The interaction of low-frequency ion-acoustic structures in relativistic degenerate plasmas: Insights from the KdV equation and the Wronskian technique

In this investigation, the nonlinear low-frequency ion-acoustic waves (IAWs) are examined in a fully relativistic, partially degenerate plasma in the presence of electron trapping in dense astrophysical environments such as white dwarfs. Using the reductive perturbation technique, the Korteweg-de Vries (KdV) equation is derived, and a generalized Wronskian technique is applied to obtain finite- and infinite-amplitude solutions. In addition, both the non-relativistic and ultra-relativistic limits are investigated. The impact of a finite electron temperature on the nonlinearity and dispersion coefficients is reported. Also, the effect of the non-relativistic, ultra-relativistic, and completely relativistic regimes on the soliton profile is examined and compared with each other. In this novel study, we discuss that the degenerate gas’s specific heat is responsible for our system’s anomalous behavior. The robust interaction of solitons with periodic singularities (known in the literature as positons) reveals their ability to maintain structural integrity, which also indirectly confirms the integrability of the KdV equation. The present findings are a step forward in enhancing our understanding of wave dynamics in dense physical environments and could pave the way for interesting practical applications in the future.