# Time-Fractional KdV Equation for the plasma in auroral zone using Variational Methods - Nonlinear Sciences > Pattern Formation and Solitons

Time-Fractional KdV Equation for the plasma in auroral zone using Variational Methods - Nonlinear Sciences > Pattern Formation and Solitons - Download this document for free, or read online. Document in PDF available to download.

Abstract: The reductive perturbation method has been employed to derive the Korteweg-deVries KdV equation for small but finite amplitude electrostatic waves. TheLagrangian of the time fractional KdV equation is used in similar form to theLagrangian of the regular KdV equation. The variation of the functional of thisLagrangian leads to the Euler-Lagrange equation that leads to the timefractional KdV equation. The Riemann-Liouvulle definition of the fractionalderivative is used to describe the time fractional operator in the fractionalKdV equation. The variational-iteration method given by He is used to solve thederived time fractional KdV equation. The calculations of the solution withinitial condition A0*sechcx^2 are carried out. Numerical studies have beenmade using plasma parameters close to those values corresponding to the daysideauroral zone. The effects of the time fractional parameter on the electrostaticsolitary structures are presented.

Author: ** El-Said A. El-Wakil, Essam M. Abulwafa, Emad K. Elshewy, Aber A. Mahmoud**

Source: https://arxiv.org/