Master's Thesis from the year 2015 in the subject Physics - Other, grade: A+ (4.00 on a scale of 4.00), Jahangirnagar University, course: Plasma Physics, language: English, abstract: The nonlinear propagation of electromagnetic (EM) waves in a pair plasma consisting of electron-positron (e-p) has been rigorously investigated in rotating astrophysical objects (e.g. pulsar magnetosphere). Two nonlinear approaches have been used to analyze the nonlinear wave phenomena in pulsar magnetosphere. The reductive perturbation method has been employed in order to derive the Korteweg-de Vries (K-dV) and derivative nonlinear Schrodinger equation (DNSE) as well as Wentzel, Kramers, and Brillouin (W.K.B) approximation technique has also been used to derive nonlinear Schrodinger equation (NLSE). The steady-state solutions of these nonlinear equations have been obtained and analyzed theoretically and numerically. The existence of solitary waves (SWs) in e-p plasma is found depending on the basic plasma parameters of considered e-p plasma. It has been seen that the basic features of SWs are significantly modified by the effects of rotational frequency (RF) and positron-to-electron thermal energy ratio (ER). The results, which have been found in this dissertation are summarized as follows: (i). e-p plasma medium supports low phase speed, high frequency, compressional e-p Alfven (CEPA) waves, and shear e-p Alfven (SEPA) waves; (ii). Both the amplitude and the width of CEPA, and SEPA SWs are seen to increase with the increase of ER. It is investigated that the RF does not have any influence on the amplitude and width of the K-dV and DNSE SWs observed in the e-p plasma of crab pulsar but the RF has a significant effect on the basic properties of SWs obtained via NLSE; (iii). The frequency of EM waves propagated in the crab pulsar lies in the range of radio waves. It is also observed that the phase speed of the EM waves increases with the decreasing values of the angle between the magnetic moment and the rotational axis, and waves are modulationally unstable when W.K.B technique has been used. The findings of these investigations may use to understand the nonlinear EM waves phenomena in rotating astrophysical and laboratory plasmas.