Spherical Solitons

Maxon, S.; Viecelli, J. A.

doi:10.1103/physrevlett.32.4

Cited by 272 publications

(129 citation statements)

References 6 publications

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“…5,6 At the risk of repeating well known knowledge, we note that the ionacoustic dispersion relation is 15…”

Section: Basics Of Reductive Perturbation Theorymentioning

confidence: 99%

“…For clarity, we shall briefly list the basic equations for one-dimensional electrostatic waves in a plasma with cold fluid protons and Boltzmann electrons, 5 in the usual ion acoustic normalized form 12…”

Section: Linear Wavesmentioning

confidence: 99%

“…5,6 None of the authors other than Maxon and Viecelli even tried to justify their approach, a majority do not even acknowledge the sources for this stretching, obviously considering it as being on par with the plane-wave stretching of Washimi and Taniuti, 2 often also without explicit reference to the originators. Almost all forget the severe restrictions mentioned by Maxon and Viecelli on its validity.…”

Section: Introductionmentioning

confidence: 99%

“…The same goes for the interpretation of other details of the experiments in terms of the theoretical predictions of the Maxon-Viecelli theory. 5,6 Unfortunately, close scrutiny of the Maxon-Viecelli approach indicates that it includes some steps which restrict its validity to a very limited range of parameter values. This aspect has inevitably been ignored in later papers, whether the authors cite the original papers or not.…”

Section: Introductionmentioning

confidence: 99%

“…In an initial pair of papers, Maxon and Viecelli 5,6 introduced a form of stretching which they applied to the study of spherically and cylindrically symmetric ion-acoustic waves, respectively. Particularly over the last decade or so, these were followed by a flood of papers using their approach, whether actually citing their papers or not.…”

Section: Introductionmentioning

confidence: 99%

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Stringent limitations on reductive perturbation studies of nonplanar acoustic solitons in plasmas

Verheest

Hellberg

2016

Physics of Plasmas

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More than fifty years ago, the Korteweg-de Vries equation was shown to describe not only solitary surface waves on shallow water, but also nonlinear ion-acoustic waves. Because of the algorithmic ease of using reductive perturbation theory, intensive research followed on a wide range of wave types. Soon, the formalism was extended to nonplanar modes by introducing a stretching designed to accommodate spherically and cylindrically symmetric ion-acoustic waves. Over the last two decades many authors followed this approach, but almost all have ignored the severe restrictions in parameter space imposed by the Ansatz. In addition, for other steps in the formalism, the justification is often not spelled out, leading to effects that are physically undesirable or ambiguous. Hence, there is a need to critically assess this approach to nonplanar modes and to use it with the utmost care, respecting the restrictions on its validity. Only inward propagation may be meaningfully studied and respect for weak nonlinearities of at most 1/10 implies that one cannot get closer to the axis or centre of symmetry than about 30 Debye lengths. Thus, one is in a regime where the modes are quasi-planar and not particularly interesting. Most papers disregard these constraints and hence reach questionable conclusions. Published by AIP Publishing.

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“…5,6 At the risk of repeating well known knowledge, we note that the ionacoustic dispersion relation is 15…”

Section: Basics Of Reductive Perturbation Theorymentioning

confidence: 99%

Section: Linear Wavesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stringent limitations on reductive perturbation studies of nonplanar acoustic solitons in plasmas

Verheest

Hellberg

2016

Physics of Plasmas

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Spherical and Cylindrical Solitons in a Warm and Multi‐Electron Plasma

Kalita

Bujarbarua

1982

Contrib Plasma Phys

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Planar and Nonplanar Shock Waves in a Degenerate Quantum Plasma

Ema

Hossen

Mamun

2015

Contrib. Plasma Phys.

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The nonlinear propagation of modified electron-acoustic (mEA) shock waves in an unmagnetized, collisionless, relativistic, degenerate quantum plasma (containing non-relativistic degenerate inertial cold electrons, both nonrelativistic and ultra-relativistic degenerate hot electron and inertial positron fluids, and positively charged static ions) has been investigated theoretically. The well-known Burgers type equation has been derived for both planar and nonplanar geometry by employing the reductive perturbation method. The shock wave solution has also been obtained and numerically analyzed. It has been observed that the mEA shock waves are significantly modified due to the effects of degenerate pressure and other plasma parameters arised in this investigation. The properties of planar Burgers shocks are quite different from those of nonplanar Burgers shocks. The basic features and the underlying physics of shock waves, which are relevant to some astrophysical compact objects (viz. non-rotating white dwarfs, neutron stars, etc.), are briefly discussed.

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Spherical Solitons

Cited by 272 publications

References 6 publications

Stringent limitations on reductive perturbation studies of nonplanar acoustic solitons in plasmas

Stringent limitations on reductive perturbation studies of nonplanar acoustic solitons in plasmas

Spherical and Cylindrical Solitons in a Warm and Multi‐Electron Plasma

Planar and Nonplanar Shock Waves in a Degenerate Quantum Plasma

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