The nonlinear propagation of electrostatic perturbation modes in an unmagnetized, collisionless, relativistic, degenerate plasma (containing both nonrelativistic and ultrarelativistic degenerate electrons, nonrelativistic degenerate ions, and arbitrarily charged static heavy ions) has been investigated theoretically. The Korteweg-de Vries (K-dV) equation has been derived by employing the reductive perturbation method. Their solitary wave solution is obtained and numerically analyzed in case of both planar and nonplanar (cylindrical and spherical) geometry. It has been observed that the ion-acoustic (IA) and modified ion-acoustic (mIA) solitary waves have been significantly changed due to the effects of degenerate plasma pressure and number densities of the arbitrarily charged heavy ions. It has been also found that properties of planar K-dV solitons are quite different from those of nonplanar K-dV solitons. There are numerous variations in case of mIA solitary waves due to the polarity of heavy ions. The basic features and the underlying physics of IA and mIA solitary waves, which are relevant to some astrophysical compact objects, are briefly discussed. 1. Introduction A large fraction of matter in the universe is in the plasma state. Significant attention has been devoted to the study of ion-acoustic (IA) waves in plasmas not only from an academic point of view, but also from the view of its vital role in understanding the nonlinear features of localized electrostatic disturbances in laboratory and space environments [1–6]. The basic features of solitary waves associated with IA waves, in which electron thermal pressure gives rise to a restoring force and ion mass provides the inertia, were first theoretically predicted by Washimi and Tanuiti by assuming an ideal plasma containing cold ions and isothermal electrons. These basic features [7] were verified by a novel laboratory experiment of Ikezi et al. [6]. Presently, relativistic degeneracy of plasmas has received great attention because of its vital role in different astrophysical environments [8, 9], where particle velocities become comparable to the speed of light. Astrophysical compact objects such as white dwarfs, neutron stars, quasars, black holes, and pulsars are examples where relativistic degenerate plasmas are dominant and interesting new phenomena are investigated by several nonlinear effects in such plasmas. The basic constituents of white dwarfs are mainly oxygen, carbon, and helium with an envelope of hydrogen gas. In some relatively massive white dwarfs, one can think of the presence
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