Time-Fractional KdV Equation Describing the Propagation of Electron-Acoustic Waves in plasma

TL;DR

This paper derives a time-fractional KdV equation for electron-acoustic waves in plasma using variational principles and solves it with the variational-iteration method, highlighting potential applications in Earth's magnetotail.

Contribution

It introduces a novel time-fractional KdV model for plasma waves and applies a variational-iteration method for its solution, extending classical models with fractional calculus.

Findings

Solution obtained with initial condition A0*sech(cx)^2

Model applicable to Earth's magnetotail plasma environment

Demonstrates the use of fractional calculus in plasma wave modeling

Abstract

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electron-acoustic waves. 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 the Earth's magnetotail region.