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    Exact Solutions of the Gardner Equation and their Applications to the Different Physical Plasmas
    (SPRINGER, 2016) Daghan, D.; Donmez, O.
    Traveling wave solution of the Gardner equation is studied analytically by using the two dependent (G (')/G,1/G)-expansion and (1/G ('))-expansion methods and direct integration. The exact solutions of the Gardner equations are obtained. Our analytic solutions are applied to the unmagnetized four-component and dusty plasma systems consisting of hot protons and electrons to investigate dynamical features of the solitons and shock waves produced in these systems. A wide variety of parameters of the plasma is used, and the basic features of the Gardner solitons that are beyond the existing study in literature are found. It is observed that the analytic solutions from (G (')/G,1/G)-expansion and (1/G ('))-expansion methods only produce shock waves but the solitary waves are found from the analytic solutions derived from the direct integration. It is also noted that the superhot electrons and relative mass density of the electrons significantly effect the soliton's amplitude, width, and position. We have also numerically proved that the combination of every value of nomalized density mu (1) or temperature ratio sigma (1) with the other sets of plasma parameters creates a region where the solutions have similar physical properties. The time-dependent behavior of the soliton is also studied, and a periodic motion of soliton along the phase variable eta is found during the evolution. The investigations and the limits presented in this study may be helpful for studying and understanding the nonlinear properties of the solitary and shock waves seen in various physical and astrophysical plasma systems.
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    Investigating the effect of integration constants and various plasma parameters on the dynamics of the soliton in different physical plasmas
    (AMER INST PHYSICS, 2015) Daghan, D.; Donmez, O.
    The nonlinear dynamics and propagation of ion acoustic waves in a relativistic and ideal plasmas, which have the pressure variation of electrons and ions and degenerate electrons, are investigated using the analytic solution of KdV type equations performed applying (G'/G)-expansion and (G'/G, 1/G)-expansion methods. The effects of various parameters, such as phase velocity of the ion acoustic wave, the ratio of ion temperature to electron temperature, normalized speed of light, electron and ion streaming velocities, arbitrary and integration constants, on the soliton dynamics are studied. We have found that dim and hump solitons and their amplitudes, widths and dynamics strongly depend on these plasma parameters and integration constants. The source term mu plays also a vital role in the formation of the solitons. Moreover, it is also found that the observed solitary wave solution can be excited from hump soliton to dip soliton. This dramatic change of the solitons can occur due to the various values of the integration constants and ion streaming velocities. Finally, it is important to note that the analytic solutions of the nonlinear equation, reported in this study, could be used to explain the structures of solitons in the astrophysical space and in laboratory plasmas. (C) 2015 AIP Publishing LLC.