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Variational approach to Langmuir waves described by the Zakharov equations

Published online by Cambridge University Press:  13 March 2009

J. C. Bhakta
J. C. Bhakta
Affiliation:
Department of Mathematics, University of Chittagong, Bangladesh
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Abstract

Nonlinear modulational instability and the evolution of a pulse that is initially non-solitonic for Langmuir waves described by the Zakharov equations are considered. The average Lagrangian method has been used to derive the nonlinear dispersion relation for Stokes waves. It is found that the region of instability increases with the amplitude of the perturbed Langmuir field. The propagation of the pulse is studied with the help of the Rayleigh-Ritz optimization method. It is noted that the width of the pulse oscillates rapidly for high initial pulse velocity.

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 45 , Issue 2 , April 1991 , pp. 203 - 212
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

Ablowitz, M. J., Kaup, D. J., Newell, A. C. & Segur, H. 1973 Phys. Rev. Lett. 30, 1262.CrossRefGoogle Scholar
Anderson, D., Lisak, M. & Reichel, T. 1988 J. Opt. Soc. Am. 5B, 207.CrossRefGoogle Scholar
Bhakta, J. C. 1988 J. Plasma Phys. 39, 297.CrossRefGoogle Scholar
Bhakta, J. C. 1990 Beitr. Plasmaphys. 30, 431.Google Scholar
Bhakta, J. C., Majumder, D. & Gupta, M. R. 1983 Plasma Phys. 25, 983.CrossRefGoogle Scholar
Gardner, C. S., Greene, J. M., Kruskal, M. D. & Miura, R. M. 1967 Phys. Rev. Lett. 19, 1095.CrossRefGoogle Scholar
Gardner, C. S., Greene, J. M., Kruskal, M. D. & Miura, R. M. 1974 Commun. Pure Appl. Maths, 27, 97.CrossRefGoogle Scholar
Lax, P. D. 1968 Commun. Pure Appl. Maths, 21, 467.CrossRefGoogle Scholar
Majumder, D. & Bhakta, J. C. 1985 Beitr. PlasmaPhys. 25, 633.CrossRefGoogle Scholar
Pereira, N. R., Sudan, R. N. & Deravit, J. 1977 Phys. Fluids, 20, 271.CrossRefGoogle Scholar
Thornhill, S. G. & Ter Haar, D. 1978 Phys. Rep. 43, 43.CrossRefGoogle Scholar
Weiland, J. & Wilhelmsson, H. A. 1977 Coherent Nonlinear Interaction of Waves in Plasmas. Pergamon.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley-Interseience.Google Scholar