الفهرس 
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Abstract
In this thesis, we have studied the propagation of ion acoustic solitary waves
in relativistic degenerate electron-ion plasmas. Also nonlinear electromagnetic
waves in a degenerate electron-positron plasma are investigated. Moreover, study
of higher-order corrections to nonlinear dust-ion-acoustic shock waves in a
degenerate dense space plasma is done.
In chapter 2, a reductive perturbation technique (RPT) is employed, a
rigorous study of ion acoustic solitary waves (IASWs) in dense electron-ion (EI)
plasmas is carried out leading to two evolution equations. These equations are
Korteweg-de Vries (KdV) and KdV type equations. Both of nonrelativistic and
ultrarelativistic degenerate electrons cases are considered. The higher-order
contributions of nonlinear and dispersion terms are calculated. Stationary solutions
of the derived evolution equations are estimated. Two different applications; one is
for hydrogen (H⁺) and the other is for singly charged helium (He⁺) ions, which are the main components of dense astrophysical objects (white dwarf stars), are
analyzed. It is found that the relativistic parameter, R₀, affects on the IASW phase
velocity. The higher-order corrections are included in ultrarelativistic electrons;
where it affects on both the amplitude and the shape of the produced solitary
waves. The plasma model with He⁺ ions has larger amplitude and wider width
compared to H⁺ case. These findings are devoted for explaining the observed
solitary waves propagating in the outer periphery of compact dense stars which
mostly consist of hydrogen and helium ions with degenerate electrons.
In chapter 3, the nonlinear propagation of magnetosonic solitary waves in an
ultracold, degenerate (extremely dense) electron-positron (EP) plasma (containing
ultracold, degenerate electron and positron fluids) is investigated also using a RPT.
The set of basic equations is reduced to KdV equation for the lowest-order
perturbed magnetic field and to a KdV type equation for the higher-order perturbed
magnetic field. The solutions of these evolution equations are obtained. For a
better accuracy and searching on new features, the new solutions are analyzed
numerically based on compact objects (white dwarf) parameters. It is found that
including the higher-order corrections results as a reduction (increment) of the fast
(slow) electromagnetic wave amplitude but its width is increased in both cases.The ranges where the RPT can describe adequately the total magnetic field
including different conditions are discussed. In chapter 4, a RPT is also used to study the contribution of higher-order
nonlinearity and dissipation to nonlinear dust ion acoustic (DIA) shock waves in three-component degenerate dense space plasma. The model consists of degenerate
electron (being either ultrarelativistic or nonrelativistic), nonrelativistic ion fluid
and stationary heavy dust grains. A nonlinear Burger equation and a linear
inhomogeneous Burger-type equation are derived. The present model admits only
compressive DIA shocks. Including these higher-order corrections results in
creating new solitary wave structures that we call ”humped DIA shock” waves. For the case of ultrarelativistic (nonrelativistic) electrons, one (two) humped DIA shock is (are) created. The DIA shock wave amplitude and velocity are larger in case of ultrarelativistic electrons than that of nonrelativistic electrons. It is shown that the effects of kinematic viscosity, heavy dust grains number density, and equilibrium ion number density have important roles on the basic features of the produced DIA shocks and the associated electric fields. The implications of our
results to dense plasmas in astrophysical objects (e.g., non-rotating white dwarf
stars) are discussed.
Due to introducing the higher-order nonlinear and dispersion corrections, the produced IASW solitons and DIA shocks are changed. It was found that the present findings due to incorporating these higher-order corrections show.