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Modified Korteweg–de Vries solitons at supercritical densities in two-electron temperature plasmas

Published online by Cambridge University Press:  01 April 2016

Frank Verheest ,
Carel P. Olivier  and
Willy A. Hereman
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
Carel P. Olivier
Affiliation:
Space Science, South African National Space Agency, PO Box 32, Hermanus 7200, South Africa
Willy A. Hereman
Affiliation:
Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80401-1887, USA
*
†Email address for correspondence: frank.verheest@ugent.be
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Abstract

The supercritical composition of a plasma model with cold positive ions in the presence of a two-temperature electron population is investigated, initially by a reductive perturbation approach, under the combined requirements that there be neither quadratic nor cubic nonlinearities in the evolution equation. This leads to a unique choice for the set of compositional parameters and a modified Korteweg–de Vries equation (mKdV) with a quartic nonlinear term. The conclusions about its one-soliton solution and integrability will also be valid for more complicated plasma compositions. Only three polynomial conservation laws can be obtained. The mKdV equation with quartic nonlinearity is not completely integrable, thus precluding the existence of multi-soliton solutions. Next, the full Sagdeev pseudopotential method has been applied and this allows for a detailed comparison with the reductive perturbation results. This comparison shows that the mKdV solitons have slightly larger amplitudes and widths than those obtained from the more complete Sagdeev solution and that only slightly superacoustic mKdV solitons have acceptable amplitudes and widths, in the light of the full solutions.

Type
Research Article
Information
Journal of Plasma Physics , Volume 82 , Issue 2 , April 2016 , 905820208
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Copyright
© Cambridge University Press 2016 

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