PhD Thesis

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Start date: 2010

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    Intrinsic Features of Nonlinear Waves in Dusty Plasmas
    (University of Rajshahi, 2024) Salam, Md. Abdus; Ali, M. Zulfikar; Akber, Md. Ali
    Dusty plasmas are electrically conducting ionized gases (macroscopically quasi-neutral) that comprise positively and negatively charged dust particles in addition to ions and electrons. Dusty plasmas exist in the Earth's magnetosphere, cometary tails, planetary rings, asteroid rings, rotating stars, and many other astronomical environments. In dusty plasmas, various types of nonlinear waves, such as solitary waves, shock waves, etc., may be propagated. The presence of dust particles makes the plasma system more complex. Besides, the characteristics of nonlinear waves can be substantially affected by different forces and plasma parameters. We theoretically investigate the characteristics of dust-ion-acoustic solitary and shock waves, where the plasma species follow different particle distributions. The higher-order nonlinear and dispersive (or dissipative) effects on the waves are examined. We also investigate various kinds of effects, such as magnetic, adiabatic, parametric, etc., while it is illustrated that how they change the wave characteristics. An inhomogeneous KdV-type or modified KdV-type equation is obtained for demonstrating the solitary waves, whereas an inhomogeneous modified Burgers-type equation is obtained for the shock waves. The reductive perturbation method is extensively used for incorporating the higher-order effects into the KdV, modified KdV, and modified Burgers equations. The re-normalization technique, the Abel’s theorem, and the method of variation of parameters are used for adding higher-order nonlinear and dispersive (or dissipative) effects into the solutions. We deal with the theoretical investigation of the combined effect of the magnetic field and plasma rotation on the nonlinear features of obliquely propagated dust-ion-acoustic solitary waves in a magnetized dusty plasma. From the investigation, it is found that the overall impact of the magnetic field, oblique rotation, electron temperature, and dust concentration has a crucial role in changing the amplitude, width, and phase speed of the dust-ion-acoustic solitary waves. The results are expected to be helpful in describing the rotating flows of magnetized plasma that are believed to exist in the rotating stars, the pulsar magnetosphere, and other rotating astronomical objects. We also explore the dynamic behaviors of multi-solitons as well as multi-shocks that propagate in a magnetized dusty plasma. The simplified Hirota method and the Cole-Hopf transformation are applied to construct the multi-soliton or multi-shock solutions. We observe that the magnetic field has a decreasing effect on the multi-soliton amplitudes and widths, whereas the dust concentration has an increasing effect on the amplitudes and widths of both types of waves. The obtained results might be helpful to describe the solitary and shock waves propagated in the Earth's mesosphere, Jupiter's magnetosphere, cometary tails, etc., in which dust particles are commonly seen.
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    Interaction Phenomena of Nonlinear Waves in Unmagnetized Plasmas
    (University of Rajshahi, Rajshahi, 2019) Alam, Mohammad Shah; Talukder, Mamunur Rashid; Ali, M. Hossain
    This dissertation is concerned with the study of interaction phenomena of nonlinear waves in unmagnetized plasmas. The plasma system considered is fully ionized, collisionless and homogeneous and/or inhomogeneous that contains multi-component plasma species under different situations. To investigate the physical issues of the interaction phenomena of nonlinear waves the nonlinear evolution equations are derived. The extended Poincaré-Lighthill-kue (ePLK) method is used to derive the nonlinear evolution equations. The interaction phenomena pertaining to plasma parameters on the production of ion-acoustic solitary waves, ion-acoustic shock waves and rogue waves and their consequences on phase shifts and amplitudes are investigated in different plasma situation. The interaction processes among the waves (such as ion-acoustic solitary waves, ion-acoustic shock waves) for single and multi-soliton plasmas are also studied considering the analytical solutions to the nonlinear evolution equations under some assumptions to discuss the characteristic of the waves in the plasmas that are observed in astrophysical, space and laboratory plasmas. In chapter one, some important physical terms that are relevant to the plasma phenomena are briefly discussed. Chapter two discusses the interaction phenomena of ion-acoustic multi-solition and the production of rogue waves in an unmagnetized plasmas composing non-relativistic as well as relativistic degenerate electrons and positrons, and inertial non-relativistic helium ions. The interaction phenomena are investigated by deriving two-sided Korteweg-de Vries (KdV) equations with their corresponding phase shifts employing extended Poicaré-Lighthill-Kuo (ePLK) method and to study the properties of rogue waves the nonlinear Schrödinger equation (NLSE) is obtained from the modified KdV (mKdV) equation.-------
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    Massive Particle Tunneling from Black Hole Spacetime
    (University of Rajshahi, 2013) Hossain, Md. Ilias; Rahman, M. Atiqur
    We investigate the Hawking radiation from different kind of black holes by massive particle tunneling process near the event horizon of the black hole in de Sitter and anti-de Sitter spaces. We calculate the imaginary part of the action from the relativistic Hamilton-Jacobi equation avoid by exploring the equation of motion of the radiation particle in Pain leave coordinate system in order to explore the Hawking non-thermal and purely thermal radiations. The thesis is organized as follows: In chapter 1 we give a brief discussion about our work of studying of massive particle tunneling from black hole space-time. In chapter 2 we review the relativistic Hamilton-Jacobi equation to perform our prime work. In chapter 3 to 10 we investigate the Hawking non-thermal and purely thermal radiations using massive particles tunneling process by employing Hamilton-Jacobi method for Schwarzschild-de Sitter (SdS), Schwarzschild-anti-de Sitter (SAdS), Reissner-Nordström-de Sitter (RNdS), Reissner-Nordström-anti-de Sitter (RNAdS), Kerr-de Sitter (KdS), Kerr-anti-de Sitter (KAdS), Kerr-Newman-de Sitter (KNdS) and Kerr-Newman-anti-de Sitter (KNAdS) black holes. We express the position of all kind of black holes in an infinite series in terms of black hole parameters so that the space-time metric becomes dynamical and derive the new line elements. Taking into account the energy conservation, the angular momentum conservation and the unfixed background spacetime. When self-gravitation interaction is considered, the derived emission/radiation spectrums are not purely thermal and the tunneling rates are related to the change of the Bekenstein-Hawking entropy, which satisfy an underlying unitary theory. Our new process provides an interesting correction to the Hawking pure thermal radiation of the black hole and in the limiting case, the results are accordant with that obtained by Parikh and Wilczek’s method of the black hole.
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    Solitary Wave Solutions of NLEEs in Plasma Physics and Engineering
    (University of Rajshahi, 2015) Khan, Md. Ashrafuzzaman; Akbar, Md. Ali
    Although the modified simple equation (MSE) method effectively provides exact solitary wave solutions to nonlinear evolution equations (NLEEs) in the field of applied mathematics, mathematical physics, plasma physics and engineering, it has some limitations. When the balance number is greater than one, usually the method does not give any solution. In this dissertation, we have exposed a process as to how to implement the MSE method to solve the NLEEs for balance number two. In order to verify the process, some NLEEs have been solved by means of this scheme, and we found some fresh traveling wave solutions. When the parameters receive special values, solitary wave solutions are derived from the exact traveling wave solutions and we have analyzed the solitary wave properties by the graphs of the solutions. These solitary wave solutions include soliton, kink shape soliton, singular kink shape soliton, bell shape soliton, singular bell shape soliton, anti-bell shape soliton, singular anti-bell shape soliton, etc. The attraction of the MSE method is that it is consistent, peaceful, authentic, and we found some fresh new traveling wave solutions other than the existing methods, such as, the basic (G /G) -expansion method. We emphasize the implementation of the MSE method, how to examine the solutions to NLEEs for balance number two and also compare the solutions obtained by the MSE method and the well-known existing (G /G) -expansion method. This shows the validity, usefulness, and necessity of the MSE method and our graphical representations describe the obtained traveling wave solutions.