Nonlinear propagation of ion-acoustic (IA) waves in a degenerate dense plasma (with all the constituents being degenerate, for both the non-relativistic or ultrarelativistic cases) have been investigated by the reductive perturbation method. The linear dispersion relation and Korteweg de Vries (KdV) equation have been derived, and the numerical solutions of KdV equation have been analysed to identify the basic features of electrostatic solitary structures that may form in such a degenerate dense plasma. The implications of our results in compact astrophysical objects, particularly, in white dwarfs and neutron stars, have been briefly discussed.

The properties of dust-ion-acoustic Gardner double layers (DIA GDLs) in an unmagnetized dusty plasma, whose constituents are negatively-charged stationary dust, inertial ions, and Boltzmann electrons of two distinct temperatures, are rigorously investigated by employing the reductive perturbation method: Gardner approach. The standard Gardner equation is derived, and its double layer (DL) solution is obtained. It has been shown that the properties of the DIA GDLs are significantly modified by some plasma parameters (viz. 𝜎 = 𝑇_e1/𝑇_e2, 𝜇_e1 = 𝑛_e10/𝑛_i0, and 𝜇_e2 = 𝑛_e20/𝑛_i0, where 𝑇_e1 (𝑇_e2) is the cold (hot) electron temperature, 𝑛_e10 (𝑛_e20) is the cold (hot) electron number density at equilibrium, and 𝑛_i0 is the ion number density at equilibrium). The implications of our investigation in understanding the basic features of nonlinear electrostatic perturbations observed in many space plasma systems and laboratory devices are briefly discussed.