Abstract
In this work, the model equation with space fractional-order (FO) is used to investigate the nonlinear ion acoustic shock wave excitations (NIASWEs) in an unmagnetized collisionless weakly relativistic plasma having inertial relativistic ions fluid with viscous effects, inertial-less non-thermal electrons and inertial-less Boltzmann positrons. To do it, the Korteweg-de Vries Burgers equation (KdVBE) is derived from the considered fluid model equations by implementing the standard reductive perturbation method. Accordingly, such equation is converted to space fractional KdVBE via Agrawal’s variational principle with the help of the beta fractional derivative and its properties. The exact analytical solutions of KdVBE with space FO are determined via the modified Kudryashov method. The influence of space fractional and other related plasma parameters on NIASWEs are investigated. The outcomes would be useful to understand the nature of shocks with the presence of non-local or local space in many astrophysical and space environments (especially in the relativistic wind of pulsar magnetosphere, polar regions of neutron stars, etc.) and further laboratory verification.
Highlights
It is well established that the relativistic electron-positron-ion (REPI) plasmas are existed in the evolution of the early Universe [1, 2] and in many astrophysical and space environments (ASEs), especially in the relativistic wind of pulsar magnetosphere [3], polar regions of neutron stars [4], pulsar magnetospheres [5], inner regions of the accretion disks surrounding the central black holes [6], active galactic nuclei [7], the center of the Milky Way galaxy [8], laser–plasma interaction [9, 10], and so on
In all previous studies [16, 18, 24,25,26,27], the authors have reported the influence of plasma parameters on nonlinear ion acoustic shock wave excitations (NIASWEs) in the relativistic plasmas by deriving nonlinear evolution equations (NLEEs) of integer order for the case of the locality and conservative energies of plasma particles
The analytical solutions of this equation have obtained via the effective MKM
Summary
It is well established that the relativistic electron-positron-ion (REPI) plasmas are existed in the evolution of the early Universe [1, 2] and in many astrophysical and space environments (ASEs), especially in the relativistic wind of pulsar magnetosphere [3], polar regions of neutron stars [4], pulsar magnetospheres [5], inner regions of the accretion disks surrounding the central black holes [6], active galactic nuclei [7], the center of the Milky Way galaxy [8], laser–plasma interaction [9, 10], and so on. In all previous studies [16, 18, 24,25,26,27], the authors have reported the influence of plasma parameters on nonlinear ion acoustic shock wave excitations (NIASWEs) in the relativistic plasmas by deriving NLEEs of integer order for the case of the locality and conservative energies of plasma particles. Hafez [21] has been reported the electrostatic shock wave structures in an unmagnetized collisonless plasmas by composing of the generalized distributed electrons, Boltzmann distributed positrons and relativistic ions fluid having kinetic viscous effects.
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