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Higher order nonlinear evolution equations for a three-dimensional electromagnetic wave packet in a plasma

Published online by Cambridge University Press:  12 October 2004

DEBALINA CHAKRABORTY  and
K. P. DAS
DEBALINA CHAKRABORTY
Affiliation:
Department of Mathematics, Charu Chandra College, 22 Lake Road, Calcutta 700 029, India
K. P. DAS
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Calcutta 700 009, India
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Abstract

Starting from the full set of governing equations including the weak relativistic effect, three coupled nonlinear equations with higher order nonlinear and dispersive terms are derived, which describe the nonlinear evolution of a three-dimensional electromagnetic wave packet propagating in a plasma. Two particular cases are considered, where the space dependence of the dependent variables is either on the space coordinate along the direction of propagation of the wave or on that along an arbitrary fixed direction. In both cases the three coupled equations reduce to a single equation. This single equation is used to study the modulational instability of a uniform electromagnetic wave train. It is found that due to the inclusion of the weak relativistic effect there is always modulational instability, and a higher order nonlinear term in the evolution equation has a stabilizing influence.

Type
Papers
Information
Journal of Plasma Physics , Volume 70 , Issue 5 , October 2004 , pp. 635 - 644
Copyright
2004 Cambridge University Press

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