Ion-Acoustic Waves in Unmagnitized Collisionless Weakly Relativistic Plasma using Time-Fractional KdV Equation

TL;DR

This paper derives and solves a time-fractional KdV equation for ion-acoustic waves in weakly relativistic, collisionless plasma, using variational methods and fractional calculus, with potential applications to ionospheric plasma environments.

Contribution

It introduces a novel time-fractional KdV model for plasma waves and applies variational-iteration methods to solve it, extending traditional plasma wave analysis.

Findings

Solution obtained with initial sech^2 profile

Model applicable to ionospheric plasma environments

Fractional calculus provides new insights into plasma wave dynamics

Abstract

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic ion-acoustic waves in unmagnitized collisionless weakly relativistic warm plasma. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. The result of the present investigation may be applicable to some plasma environments, such as ionosphere.