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Weakly nonlinear dispersive waves: group velocity

Published online by Cambridge University Press:  13 March 2009

Bhimsen K. Shivamoggi
Bhimsen K. Shivamoggi
Affiliation:
Department of Theoretical Physics, Research School of Physical Sciences, The Australian National University, Canberra, Australia
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Abstract

For slowly varying wave trains in a linear system, it is known that a quantity proportional to the square of the amplitude propagates with the group velocity. It is shown here, by considering a specific problem of longitudinal waves in a hot electron-plasma and using an asymptotic analysis, that this result continues to be valid even when weak nonlinearities are introduced into the system provided they produce slowly varying wave trains. The method of analysis fails, however, for weakly nonlinear ion-acoustic waves.

Type
Research Article
Information
Journal of Plasma Physics , Volume 27 , Issue 3 , June 1982 , pp. 507 - 514
Copyright
Copyright © Cambridge University Press 1982

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References

REFERENCES

Davidson, R. C. 1972 Methods of Nonlinear Plasma Theory. Academic.Google Scholar
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Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley-Interscience.Google Scholar