Dissipative Nonlinear Structures in a Dense Relativistic-Degenerate Plasma

This work examines the linear and nonlinear properties of ion-acoustic excitations in dense relativistic-degenerate plasma of astrophysical regime, composed of ultra-relativistic degenerate electrons and non-relativistic degenerate ions under collisional condition.

The study first explores unidirectional ion-acoustic solitary waves in unmagnetized collisional plasma, incorporating quantum and relativistic effects. A linear dispersion relation is derived by linearizing the scaled evolution equations. Nonlinear analysis using the reductive perturbation technique shows that, in the weak dissipation limit, the low-frequency ion-acoustic excitations are governed by a damped Korteweg-de Vries equation. An analytical solution to the KdV equation is obtained using the generalized pseudo-potential method. Since the said equation can't be solved analytically, soliton perturbation technique is applied to obtain an approximate time-varying solution.

The model is then extended to investigate three-dimensional ion-acoustic solitary structures using the multi-scale perturbation technique, deriving a damped Kadomtsev-Petviashvili equation. Time-varying solutions reveal that the soliton's velocity, amplitude, and energy decay exponentially, flattening out after traveling a finite distance. The study has a particular relevance with degenerate plasmas in ultra-dense astrophysical objects.