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Evolution of wave packets in magnetohydrodynamics

Published online by Cambridge University Press:  13 March 2009

Anju Pusri  and
S. K. Malik
Anju Pusri
Affiliation:
Department of Mathematics, Panjab University, Chandigarh-160014, India
S. K. Malik
Affiliation:
Department of Mathematics, Panjab University, Chandigarh-160014, India
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Abstract

The propagation of wave packets on the surface of an electrically conducting fluid of uniform depth in the presence of a tangential magnetic field is investigated in (2 + 1) dimensions. The evolution of wave envelope is governed by two coupled partial differential equations with cubic nonlinearity. The stability analysis reveals the existence of different regions of instability. The effect of the applied magnetic field is not only significant but also different for different regions of stability. ‘Envelope soliton’ and ‘waveguide’ solutions of the amplitude equation are also discussed. The self-focusing phenomenon that arises when the amplitude of the wave becomes infinite in finite time is also examined. It is found that in a certain region of the stability diagram it may be easier to observe this phenomenon in the presence of a magnetic field. The Rayleigh-Taylor problem is also studied and various criteria for the existence of instability are obtained.

Type
Research Article
Information
Journal of Plasma Physics , Volume 53 , Issue 2 , April 1995 , pp. 145 - 167
Copyright
Copyright © Cambridge University Press 1995

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