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Advances in Mathematical Physics
Volume 2012 (2012), Article ID 529121, 12 pages
Research Article

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

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

Received 31 March 2012; Accepted 19 June 2012

Academic Editor: Wen Xiu Ma

Copyright © 2012 S. A. El-Wakil et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.