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Asymptotic analysis of solitons and double layers at the acoustic speed

Published online by Cambridge University Press:  16 November 2017

Carel P. Olivier ,
Frank Verheest  and
Shimul K. Maharaj
Carel P. Olivier*
Affiliation:
Centre for Space Research, North-West University, Potchefstroom 2520, South Africa
Frank Verheest
Affiliation:
Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281, B–9000 Gent, Belgium School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4000, South Africa
Shimul K. Maharaj
Affiliation:
South African National Space Agency (SANSA) Space Science, P. O. Box 32, Hermanus 7200, South Africa Department of Physics, University of the Western Cape, Robert Sobukwe Road, Bellville 7535, South Africa
*
†Email address for correspondence: carel.olivier@nwu.ac.za
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Abstract

In this paper, we consider the asymptotic behaviour of solitons and double layers. By using the Sagdeev pseudopotential formalism, a Taylor series expansion is used to derive the asymptotic behaviour. For solitons and supersolitons that propagate faster than the acoustic speed, an exponential decay rate is derived. In contrast, for acoustic speed solitons and supersolitons, we show that the decay rate is algebraic, resulting in much fatter tails. These results can be extended to double layers. However, the double layer velocity affects only one side of the tail. The other side of the tail is affected by the multiplicity of the double layer root. All the results are illustrated by means of a case study.

Keywords

plasma nonlinear phenomenaplasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 6 , December 2017 , 905830605
Copyright
© Cambridge University Press 2017 

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