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Nonlinear Waveforms for Ion‐Acoustic Waves in Weakly Relativistic Plasma of Warm Ion‐Fluid and Isothermal Electrons

Author

Listed:
  • S. A. El-Wakil
  • Essam M. Abulwafa
  • E. K. El-Shewy
  • H. G. Abdelwahed
  • Hamdi M. Abd-El-Hamid

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 weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell‐shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called “blowup” solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties (namely, the amplitude and the width) of the ion‐acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region.

Suggested Citation

  • S. A. El-Wakil & Essam M. Abulwafa & E. K. El-Shewy & H. G. Abdelwahed & Hamdi M. Abd-El-Hamid, 2012. "Nonlinear Waveforms for Ion‐Acoustic Waves in Weakly Relativistic Plasma of Warm Ion‐Fluid and Isothermal Electrons," Advances in Mathematical Physics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlamp:v:2012:y:2012:i:1:n:529121
    DOI: 10.1155/2012/529121
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    References listed on IDEAS

    as
    1. He, Ji-Huan & Abdou, M.A., 2007. "New periodic solutions for nonlinear evolution equations using Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1421-1429.
    2. El-Shewy, E.K., 2005. "Effect of higher-order nonlinearity to nonlinear electron-acoustic solitary waves in an unmagnetized collisionless plasma," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1073-1079.
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