https://doi.org/10.1140/epjd/e2008-00205-1
Applications of elliptic functions to ion-acoustic plasma waves
1
Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
2
Mathematics Department, Faculty of Science, Minia University, El-Minia, Egypt
3
Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Muscat, Sultanate of Oman
4
School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P.R. China
Corresponding author: a khater_ah@hotmail.com
Received:
8
March
2008
Revised:
22
August
2008
Published online:
31
October
2008
New several classes of exact solutions are obtained in terms of the Weierstrass elliptic function for some nonlinear partial differential equations modeling ion-acoustic waves as well as dusty plasmas in laboratory and space sciences. The Weierstrass elliptic function solutions of the Schamel equation, a fifth order dispersive wave equation and the Kawahara equation are constructed. Moreover, Jacobi elliptic function solutions and solitary wave solutions of the Schamel equation are also given. The stability of some periodic wave solutions is computationally studied.
PACS: 02.30.Jr – Partial differential equations / 02.30.Ik – Integrable systems / 52.27.Lw – Dusty or complex plasmas; plasma crystals / 52.35.Fp – Electrostatic waves and oscillations
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008
