Abstract
In this paper, the fractional order models are used to study the propagation of ion-acoustic waves in ultrarelativistic plasmas in nonplanar geometry (cylindrical). Firstly, according to the control equations, (2 + 1)-dimensional (2D) cylindrical Kadomtsev–Petviashvili (CKP) equation and 2D cylindrical-modified Kadomtsev–Petviashvili (CMKP) equation are derived by using multiscale analysis and reduced perturbation methods. Secondly, using the semi-inverse method and the fractional variation principle, the abovementioned equations are derived the time-space fractional equations (TSF-CKP and TSF-CMKP). Furthermore, based on the fractional order transformation, the 1-decay mode solution of the TSF-CKP equation is obtained by using the simplified homogeneous balance method, and using the generalized hyperbolic-function method, the exact analytic solution of TSF-CMKP equation is obtained. Finally, the effects of the phase speedλ, electron number density (throughβ3) and the fractional orderα,β,ωon the propagation of ion-acoustic waves in ultrarelativistic plasmas are analyzed.
Highlights
In recent years, plasma physics [1,2,3,4] has developed rapidly in the global environment, electromagnetic propagation, and especially in the astronomical environment
An example of the first category is a white dwarf supported by the pressure of degenerate electrons, the interior of which is close to a dense solid, and an example of the second category is a neutron star supported by the pressure of nuclear degeneracy and nuclear interaction, which is close to a giant atomic nucleus
In a white dwarf, the degenerate electron number density can reach the order of 1030 cm− 3, which is expected to be degenerated in a white dwarf of sufficient quality
Summary
Plasma physics [1,2,3,4] has developed rapidly in the global environment, electromagnetic propagation, and especially in the astronomical environment. An example of the first category is a white dwarf supported by the pressure of degenerate electrons, the interior of which is close to a dense solid (ionic lattice surrounded by degenerate electrons, possibly other heavy particles or dust), and an example of the second category is a neutron star supported by the pressure of nuclear degeneracy and nuclear interaction, which is close to a giant atomic nucleus (mixture of nucleon and electron interactions, possibly other elementary particles and condensates) In such a compact object, the degenerate electron number density is very high.
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