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

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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.
Keywords
ACOUSTIC DOUBLE-LAYERS, SOLITARY WAVE SOLUTIONS, 2-ELECTRON-TEMPERATURE PLASMA, 2-TEMPERATURE ELECTRONS, GENERALIZED KDV, ION, EQUATIONS, AMPLITUDE, LAWS

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Citation

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

Chicago
Verheest, Frank, Carel P Olivier, and Willy A Hereman. 2016. “Modified Korteweg-de Vries Solitons at Supercritical Densities in Two-electron Temperature Plasmas.” Journal of Plasma Physics 82 (2).
APA
Verheest, F., Olivier, C. P., & Hereman, W. A. (2016). Modified Korteweg-de Vries solitons at supercritical densities in two-electron temperature plasmas. JOURNAL OF PLASMA PHYSICS, 82(2).
Vancouver
1.
Verheest F, Olivier CP, Hereman WA. Modified Korteweg-de Vries solitons at supercritical densities in two-electron temperature plasmas. JOURNAL OF PLASMA PHYSICS. 2016;82(2).
MLA
Verheest, Frank, Carel P Olivier, and Willy A Hereman. “Modified Korteweg-de Vries Solitons at Supercritical Densities in Two-electron Temperature Plasmas.” JOURNAL OF PLASMA PHYSICS 82.2 (2016): n. pag. Print.
@article{8053849,
  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.},
  articleno    = {905820208},
  author       = {Verheest, Frank and Olivier, Carel P and Hereman, Willy A},
  issn         = {0022-3778},
  journal      = {JOURNAL OF PLASMA PHYSICS},
  language     = {eng},
  number       = {2},
  pages        = {13},
  title        = {Modified Korteweg-de Vries solitons at supercritical densities in two-electron temperature plasmas},
  url          = {http://dx.doi.org/10.1017/S0022377816000349},
  volume       = {82},
  year         = {2016},
}

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