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On the nonlinear development of the Langmuir modulational instability

Published online by Cambridge University Press:  13 March 2009

R. O. Dendy  and
D. Ter Haar
R. O. Dendy
Affiliation:
Department of Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, U.K.
D. Ter Haar
Affiliation:
Department of Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, U.K.
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Abstract

Using the Zakharov equations in their Fourier-transformed form, we consider the development of the modulational instability (MI) both for the monochromatic and the finite-width cases. In the static approximation and considering a monochromatic Langmuir wave which is coupled only to a single pair of Stokes and anti-Stokes Langmuir perturbations, we show that the resultant set of equations is integrable and we discuss the analytical solution of these equations. We show how a finite-width driver will lead to a threshold for the MI. We compare our results with those obtained by other authors.

Type
Research Article
Information
Journal of Plasma Physics , Volume 31 , Issue 1 , February 1984 , pp. 67 - 79
Copyright
Copyright © Cambridge University Press 1984

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References

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