الفهرس 
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Abstract
Abstract
Based on a hydrodynamic model, nonlinear Schrödinger (NLS) equation for low frequency limit is derived for magnetosonic rogue waves propagating in an electron- ion plasma. The first- and second-order rogue wave solutions of the NLS equation are obtained analytically and the physical parameters effects are examined numerically. It is found that for high plasma number density and strong magnetic field the nonlinear coefficient decreases, which causes the rogue wave amplitude becomes shorter. However, the electron temperature pumping more energy to the background waves, which are sucked to create rogue waves with taller amplitudes.
Dust grain are large-size species that could be presented in plasma both in space and in laboratory. These particles would lead to change the behavior of an electron-ion plasma, so that new modes will appear as well. One of these new modes is the dust acoustic wave (DAW) in strongly coupled dusty plasma. The DAW has very slow time scale as a result of the balance between the dust grain inertia and plasma pressure. In chapter three, the nonlinear features of the DAWs in a strongly coupled unmagnetized dusty plasma containing electrons and ions following q-nonextensive distribution, and negatively charged mobile dust grains are investigated by using the reductive perturbation method. The physical parameters effects, such as q-parameter, temperature, and dust number density on the properties of the solitary and shock waves are investigated. The conditions for the formation of solitary and shock structures are also defined.
Dust-acoustic waves which accompany a collisional strongly coupled unmagnetized negatively charged dusty plasma with Boltzmann distributed electrons and ions is studied in the fourth chapter. By using a hydrodynamic model, a Korteweg de Vries-Burgers (KdV-Burgers) equation is derived. The existence conditions of the solitary pulses are defined precisely. Furthermore, numerical calculations reveal that the DAWs damp and the damping rate depends mainly on the collision frequency. The effects of the electron-to-ion number density ratio and ion-to-electron temperature ratio on the behavior of the dust-acoustic waves are investigated.
Finally, the propagation of the DAWs in a strongly coupled dusty plasma with isothermal electrons and trapped ions is investigated. The effect of polarization force is taken into account. Linear dispersion relation for the DAWs is derived and analysed numerically. The nonlinear analysis of the DAWs is made by deriving an evolution equation describing the system. This equation is solved analytically using a tanh method indicating that solitary and shock waves can
exist. The polarization force, trapped ions, and Coulomb coupling parameter on the propagating nonlinear waves are examined. It is found that the effects of polarization force and the trapped ions, and Coulomb coupling parameter significantly modify the basic features (e.g., amplitude, width, and speed) of the DA solitary and shock waves.