A Fractional Model to Study Soliton in Presence of Charged Space Debris at Low-Earth Orbital Plasma Region

Abstract

The phenomenon of solitons characterized by nonlinear structures is widely studied in the literature due to their important implications in various fields of sciences and engineering, mainly space plasma physics. These solitons are described by nonlinear evolution equations, such as the highly nonlinear Korteweg-de Vries (KdV) and Zakharov-Kuznetsov equations. Different methods are used to search soliton solutions to these nonlinear dynamical equations and the solutions obtained are determined in general as the integration of exponential, hyperbolic, trigonometric, and rational functions. The types of solitons obtained depend on the number of related parameters, the structure of nonlinearly dispersive terms, and on the type and number of various involutions imposed on the dynamical system. In this study, we show that particular types of solitons, such as the periodic solitons, compactons, singular periodic solitons, cuspons, bright kink, and bell-shaped solitons can be obtained with and without the presence of charged space debris in at low-Earth orbital plasma region without imposing external conditions or adding higher order nonlinear terms. Our model is based on the fractional actionlike variational approach which is described in general by the fractional Boltzmann equation (FBE) that models the evolution of the particle distribution function.