Abstract:
The main purpose of the present work is to investigate how electrostatic plasma parameters
modify the nonlinear ion acoustic soliton (IAS) propagation in unmagnetized collisionless
plasma including higher order Lorentz relativistic expansion terms. The study of
IASs in an unmagnetized collisionless relativistic plasma made of relativistic ion fluids,
Cairns-distributed electrons and Cairns-distributed positrons. In one dimensional analysis,
the reductive perturbation technique is employed to reduce the dynamics of the whole
system to the Korteweg-de Vries equation (KdVE) involving various nonlinearity, whose
nonlinear and dispersion coefficients are dependent on the related plasma parameters. This
indicates that KdVEs have been derived incorporating quadratic, cubic, and quartic nonlinearities.
However, as the coefficient of KdVE associated with quadratic nonlinearity
approaches zero, the method encounters limitations. To overcome this challenge, adjustments
are made to the stretching coordinates, resulting in a cubic nonlinearity KdVE that
effectively describes soliton propagation near critical values in these plasma conditions.
Additionally, a KdVE with quartic nonlinearity is derived to model super-critical values of
specific plasma parameters in relativistic plasmas.
Previous studies have primarily focused on relativistic effects on soliton propagation using
Lorentz relativistic factor expansions up to three terms. In contrast, this thesis expands
this consideration to more higher order Lorentz relativistic expansion terms to minimize
truncation errors in modeling nonlinear soliton propagation within these plasmas. The investigation
reveals that the relativistic streaming factor significantly alters the wave potential
functions with the presence of more higher order Lorentz relativistic expansion terms.
Notably, the derived KdVE shows that quadratic nonlinearity supports both compressive
and rarefactive soliton propagation, whereas cubic and quartic nonlinearities exclusively
support compressive solitons. Furthermore, this study explores how plasma parameters, incorporating
more higher order Lorentz relativistic expansion terms, influence the amplitude
and width of IASs in the unmagnetized relativistic plasma. It finds that higher order terms
of the Lorentz relativistic factor noticeably modify the propagation characteristics of IASs
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within this specific plasma environment. The effect of plasma parameters on the amplitude
and width of IASs has also been discussed with the physical interpretations.
