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The European Physical Journal D

, Volume 50, Issue 2, pp 177–184 | Cite as

Applications of elliptic functions to ion-acoustic plasma waves

  • A. H. KhaterEmail author
  • M. M. Hassan
  • E. V. Krishnan
  • Y. Z. Peng
Nonlinear Dynamics

Abstract

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 

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Copyright information

© Springer 2008

Authors and Affiliations

  • A. H. Khater
    • 1
    Email author
  • M. M. Hassan
    • 2
  • E. V. Krishnan
    • 3
  • Y. Z. Peng
    • 4
  1. 1.Mathematics DepartmentFaculty of Science, Beni-Suef UniversityBeni-SuefEgypt
  2. 2.Mathematics DepartmentFaculty of Science, Minia UniversityEl-MiniaEgypt
  3. 3.Department of Mathematics and StatisticsSultan Qaboos UniversityMuscatSultanate of Oman
  4. 4.School of Mathematics and Statistics, Wuhan UniversityWuhanP.R. China

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