Ion-acoustic waves in plasma of warm ions and isothermal electrons using time-fractional KdV equation

doi:10.1088/1674-1056/20/4/040508

Abstract The ion-acoustic solitary wave in collisionless unmagnetized plasma consisting of warm ions-fluid and isothermal electrons is studied using the time fractional KdV equation. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude ion-acoustic wave in warm plasma. The Lagrangian of the time fractional KdV equation is used in a similar form to the Lagrangian of the regular KdV equation with fractional derivative for the time differentiation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that gives the time fractional KdV equation. The variational-iteration method is used to solve the derived time fractional KdV equation. The calculations of the solution are carried out for different values of the time fractional order. These calculations show that the time fractional can be used to modulate the electrostatic potential wave instead of adding a higher order dissipation term to the KdV equation. The results of the present investigation may be applicable to some plasma environments, such as the ionosphere plasma.

Keywords: ion-acoustic waves Euler--Lagrange equation Riemann--Liouvulle fractional derivative fractional KdV equation variational-iteration method

Received: 14 November 2010
Revised: 04 December 2010
Accepted manuscript online:

PACS:	05.45.Df	(Fractals)
	05.30.Pr	(Fractional statistics systems)

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Sayed A. El-Wakil, Essam M. Abulwafa, Emad K. El-Shewy, and Abeer A. Mahmoud Ion-acoustic waves in plasma of warm ions and isothermal electrons using time-fractional KdV equation 2011 Chin. Phys. B 20 040508

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Ion-acoustic waves in plasma of warm ions and isothermal electrons using time-fractional KdV equation

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