UNSPECIFIED. (2001) Meromorphy and topology of localized solutions in the Thomas-MHD model. JOURNAL OF PLASMA PHYSICS, 65 (Part 5). pp. 365-406. ISSN 0022-3778

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Abstract

The one-dimensional MHD system first introduced by J.H. Thomas [Phys. Fluids 11, 1245 (1968)] as a model of the dynamo effect is thoroughly studied in the limit of large magnetic Prandtl number. The focus is on two types of localized solutions involving shocks (antishocks) and hollow (bump) waves. Numerical simulations suggest phenomenological rules concerning their generation, stability and basin of attraction. Their topology, amplitude and thickness are compared favourably with those of the meromorphic travelling waves, which are obtained exactly, and respectively those of asymptotic descriptions involving rational or degenerate elliptic functions. The meromorphy bars the existence of certain configurations, while others are explained by assuming imaginary residues. These explanations are tested using the numerical amplitude and phase of the Fourier transforms as probes of the analyticity properties. Theoretically, the proof of the partial integrability backs up the role ascribed to meromorphy. Practically, predictions are derived for MHD plasmas.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Journal or Publication Title:	JOURNAL OF PLASMA PHYSICS
Publisher:	CAMBRIDGE UNIV PRESS
ISSN:	0022-3778
Date:	June 2001
Volume:	65
Number:	Part 5
Number of Pages:	42
Page Range:	pp. 365-406
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/11282

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