Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-15T18:53:28.434Z Has data issue: false hasContentIssue false
  • English
  • Français

The theory of nonlinear ion-acoustic waves revisited

Published online by Cambridge University Press:  13 March 2009

W. Malfliet  and
E. Wieërs
W. Malfliet
Affiliation:
Department of Physics, University of Antwerp (UIA), B-2610 Wilrijk, Belgium
E. Wieërs
Affiliation:
Department of Physics, University of Antwerp (UIA), B-2610 Wilrijk, Belgium
Get access Rights & Permissions [Opens in a new window]

Abstract

The basic set of equations describing nonlinear ion-acoustic waves in a cold collisionless plasma, in the limit of long wavelengths, is reconsidered. First, a travelling-wave solution is found up to third order by means of a straightforward perturbation approach based on the smallness of the wavenumber. As a result, a positive dressed solitary wave shows up, which is larger, taller and faster than the KdV soliton, the first-order result. Furthermore, the accuracy of this approach is tested and compared with previous result. Secondly, the reductive perturbation techique to study higher-order corrections is revised and adapted to the present problem.

Type
Research Article
Information
Journal of Plasma Physics , Volume 56 , Issue 3: Special Issue: Honour of David Montgomery , December 1996 , pp. 441 - 450
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Broer, L. J. F. and Sluijter, F. W. 1977 Phys. Fluids 20, 1458.CrossRefGoogle Scholar
Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic Press, New York.Google Scholar
El-Labany, S. K. 1995 J. Plasma Phys. 54, 285.CrossRefGoogle Scholar
Hershkowitz, N., Romesser, T. and Montgomery, D. 1972 Phys. Rev. Lett. 29, 1568.Google Scholar
Ichikawa, Y. H. and Watanabe, S. 1977 J. Phys. (Paris) 38, C6–15.Google Scholar
Ikezi, H., Taylor, I. and Baker, D. 1973 Phys. Rev. Lett. 25, 11.CrossRefGoogle Scholar
Kodama, Y. and Taniuti, T. 1978 J. Phys. Soc. Jpn 45, 298.Google Scholar
Malfliet, W. 1992 Am. J. Phys. 60, 650.CrossRefGoogle Scholar
Malfliet, W. and Hereman, W. 1996 Physica Scripta (to be published).Google Scholar
Scott, A. C. 1974 Backlünd Transformations (ed. Bullough, R. and Caudrey, P.), p. 80. Springer-Verlag, Berlin.Google Scholar
Sugimoto, N. and Kakutani, T. 1977 J. Phys. Soc. Jpn 43, 1469.CrossRefGoogle Scholar
Taniuti, T. 1974 Prog. Theor. Phys. Suppl. 55, 1.CrossRefGoogle Scholar
Tiwari, R. S. and Sharma, S. R. 1980 Can. J Phys. 60, 154.CrossRefGoogle Scholar
Washimi, H. and Taniuti, T. 1966 Phys. Rev. Lett. 217, 996.Google Scholar
Verheest, F. 1988 J. Plasma Phys. 39, 71.Google Scholar
Yashvir, Tiwari R. S. and Sharma, S. R. 1988 Can. J. Phys. 66, 824.CrossRefGoogle Scholar