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Asymptotic analysis of solitons and double layers at the acoustic speed

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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 phenomena, plasma waves, SOLITARY WAVES, ION, PLASMA

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Citation

Please use this url to cite or link to this publication:

Chicago
Olivier, Carel P, Frank Verheest, and Shimul K Maharaj. 2017. “Asymptotic Analysis of Solitons and Double Layers at the Acoustic Speed.” Journal of Plasma Physics 83 (6).
APA
Olivier, Carel P, Verheest, F., & Maharaj, S. K. (2017). Asymptotic analysis of solitons and double layers at the acoustic speed. JOURNAL OF PLASMA PHYSICS, 83(6).
Vancouver
1.
Olivier CP, Verheest F, Maharaj SK. Asymptotic analysis of solitons and double layers at the acoustic speed. JOURNAL OF PLASMA PHYSICS. 2017;83(6).
MLA
Olivier, Carel P, Frank Verheest, and Shimul K Maharaj. “Asymptotic Analysis of Solitons and Double Layers at the Acoustic Speed.” JOURNAL OF PLASMA PHYSICS 83.6 (2017): n. pag. Print.
@article{8540185,
  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.},
  articleno    = {905830605},
  author       = {Olivier, Carel P and Verheest, Frank and Maharaj, Shimul K},
  issn         = {0022-3778},
  journal      = {JOURNAL OF PLASMA PHYSICS},
  language     = {eng},
  number       = {6},
  pages        = {17},
  title        = {Asymptotic analysis of solitons and double layers at the acoustic speed},
  url          = {http://dx.doi.org/10.1017/s0022377817000848},
  volume       = {83},
  year         = {2017},
}

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