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Nonlinear interactions of two compressional hydromagnetic waves

Published online by Cambridge University Press:  13 March 2009

B. Ghosh  and
K. P. Das
B. Ghosh
Affiliation:
Department of Physics, R. K. Mission Vidyamandir, Belur Math, Howrah-711202, India
K. P. Das
Affiliation:
Department of Applied Mathematics, Calcutta University, 92, Acharya Prafulla Chandra Road, Calcutta-700009, India
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Abstract

Nonlinear interactions of two azimuthally symmetric compressional hydromagnetic waves propagating in a cylindrical waveguide filled with cold magnetized plasma are investigated. Two cases are considered: the nonlinear interaction of two identical oppositely propagating compressional waves and the nonlinear interaction of two compressional waves propagating with equal group velocities. In the first case the second-order perturbation fields generated through self- and mutual interactions of the waves are calculated and their effect on the otherwise-formed simple linear standing-wave pattern is studied. The possibility of observing a resonant nonlinear interaction is shown. In the second case, in order to describe the nonlinear evolution of the wave amplitudes, two coupled nonlinear Schrödinger (NLS) equations are presented. When excited individually, both the waves are seen to be modulationally stable; but when excited simultaneously, a strong nonlinear wave-wave coupling comes into play, which makes the waves modulationally unstable. The corresponding growth rate of the instability is also calculated.

Type
Research Article
Information
Journal of Plasma Physics , Volume 39 , Issue 2 , April 1988 , pp. 215 - 228
Copyright
Copyright © Cambridge University Press 1988

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