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Applied Mathematics and Mechanics

, Volume 31, Issue 1, pp 119–124 | Cite as

Dynamical behavior of traveling wave solutions of ion acoustic plasma equations

  • Shu-min Li (李庶民)Email author
  • Tian-lan He (贺天兰)
Article

Abstract

By using the theory of planar dynamical systems to the ion acoustic plasma equations, we obtain the existence of the solutions of the smooth and non-smooth solitary waves and the uncountably infinite smooth and non-smooth periodic waves. Under the given parametric conditions, we present the sufficient conditions to guarantee the existence of the above solutions.

Key words

solitary traveling wave solution periodic traveling wave solution smoothness of waves ion acoustic plasma equations 

Chinese Librarary Classification

O175.14 

2000 Mathematics Subject Classification

34A34 

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References

  1. [1]
    Haragus, M. and Scheel, A. Linear stability and instability of ion-acoustic plasmas solitary waves. Physica D 170, 13–30 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Li, Y. and Sattinger, D. H. Soliton collisions in the ion acoustic plasmas equations. Journal of Mathematics and Fluid Mechanics 1, 117–130 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Li, Jibin and Liu, Zhengrong. Smooth and non-smooth traveling waves in a nonlinearly dispersive equation. Applied Mathematical Modelling 25, 41–56 (2000)zbMATHCrossRefGoogle Scholar
  4. [4]
    Li, Jibin and Dai, Huihui. On the Study of Singular Nonlinear Travelling Wave Equations: Dynamical Approach, Science Press, Beijing (2007)Google Scholar
  5. [5]
    Perko, L. M. Bifurcation of limit cycles. Lecture Notes in Mathematics 1455, Springer-Verlag, New York, 315–333 (1990)Google Scholar

Copyright information

© Shanghai University and Springer Berlin Heidelberg 2010

Authors and Affiliations

  • Shu-min Li (李庶民)
    • 1
    • 2
    Email author
  • Tian-lan He (贺天兰)
    • 1
  1. 1.Center for Nonlinear Science StudiesKunming University of Science and TechnologyKunmingP. R. China
  2. 2.Oxbridge CollegeKunming University of Science and TechnologyKunmingP. R. China

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