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Modulations of slow sausage surface waves travelling along a magnetized slab

Published online by Cambridge University Press:  13 March 2009

I. Zhelyazko ,
K. Murawski ,
M. Goossens ,
P. Nenovaki  and
B. Roberts
I. Zhelyazko
Affiliation:
Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Leuven, Belgium
K. Murawski
Affiliation:
Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Leuven, Belgium
M. Goossens
Affiliation:
Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Leuven, Belgium
P. Nenovaki
Affiliation:
Institute for Space Research, BG-1000 Sofia, Bulgaria
B. Roberts
Affiliation:
Department of Mathematical and Computational Sciences, University of St Andrews, St Andrews KY16 9SS, Fife, Scotland
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Abstract

In this paper we consider a set of nonlinear MHD equations that admits in a linear approximation a solution in the form of a slow sausage surface wave travelling along an isolated magnetic slab. For a wave of small but finite amplitude, we investigate how a slowly varying amplitude is modulated by nonlinear self-interactions. A stretching transformation shows that, at the lowest order of an asymptotic expansion, the original set of equations with appropriate boundary conditions (free interfaces) can be reduced to the cubic nonlinear Schrödinger equation, which determines the amplitude modulation. We study analytically and numerically the evolution of impulsively generated waves, showing a transition of the initial states into a train of solitons and periodic waves. The possibility of the existence of solitary waves in the solar atmosphere is also briefly discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 51 , Issue 2 , April 1994 , pp. 291 - 308
Copyright
Copyright © Cambridge University Press 1994

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