Abstract
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.
Highlights
A large fraction of matter in the universe is in the plasma state
−ρ, ρ = ni − (1 + jμ) ne + jμ, where ] = 0 for one-dimensional planar geometry and ] = 1(2) for nonplanar cylindrical geometry; ni is the ion number densities normalized by its equilibrium value ni0, ui is the ion fluid speed normalized by Ci =1/2 with me being the electron rest mass, c is the speed of light in vacuum, and φ is the electrostatic wave potential normalized by mec2/e with e being the magnitude of the charge of an electron
In order to analyze the IA and modified ion-acoustic (mIA) solitary waves, we turn to (9) with the term ]φ(1)/2τ, which is due to the effects of the nonplanar geometry
Summary
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 from an academic point of view, and from the view of its vital role in understanding the nonlinear features of localized electrostatic disturbances in laboratory and space environments [1,2,3,4,5,6]. Shukla et al [27] theoretically investigated the nonlinear propagation of electrostatic waves in degenerate quantum plasma They considered strongly coupled nondegenerate ions and degenerate electron fluids in an unmagnetized dense plasma and studied the basic properties of solitary and shock structures. Zobaer et al [9, 15, 16, 29] considered nonrelativistic ion fluids and both nonrelativistic and ultrarelativistic electron fluids and theoretically investigated the basic features of solitary, shock, and double layer structures All of these investigations are mainly based on planar geometry and they did not consider the effect of heavy ions, which may not be a realistic situation in space environments. In our present work, we attempt to study the basic features of planar and nonplanar IA and mIA solitary waves by deriving the Korteweg-de Vries equation in a dense plasma containing degenerate electron and ion fluids and arbitrarily charged static heavy ions.
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