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

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

中国物理B ›› 2011, Vol. 20 ›› Issue (4): 40508-040508.doi: 10.1088/1674-1056/20/4/040508

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

Sayed A. El-Wakil, Essam M. Abulwafa, Emad K. El-Shewy, Abeer A. Mahmoud

State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China

收稿日期:2010-11-14 修回日期:2010-12-04 出版日期:2011-04-15 发布日期:2011-04-15

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

Sayed A. El-Wakil^†, Essam M. Abulwafa, Emad K. El-Shewy, and Abeer A. Mahmoud

Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received:2010-11-14 Revised:2010-12-04 Online:2011-04-15 Published:2011-04-15

摘要/Abstract

摘要： 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.

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.

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

中图分类号: (Fractals)

05.45.Df

05.30.Pr (Fractional statistics systems)

Sayed A. El-Wakil, Essam M. Abulwafa, Emad K. El-Shewy, Abeer A. Mahmoud. Ion-acoustic waves in plasma of warm ions and isothermal electrons using time-fractional KdV equation[J]. 中国物理B, 2011, 20(4): 40508-040508.

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[J]. Chin. Phys. B, 2011, 20(4): 40508-040508.

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

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

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