Reflection of a cylindrical ion-acoustic soliton at a symmetric axis

Tsukabayashi, Isao; Nakamura, Yoshiharu; Ogino, T.

doi:10.1016/0375-9601(81)90452-7

Cited by 15 publications

(5 citation statements)

References 8 publications

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“…Specifically, it is well known that the radial part of the solutions to the cylindrically symmetric wave equation is given by Hankel functions of order zero, 9,22,23 usually denoted by H 1 0 ðkrÞ and H 2 0 ðkrÞ, respectively. Fortunately, the cylindrically symmetric case can be saved in the asymptotic limit kr ) 1.…”

Section: Aspects Of the Standard Wave Equationmentioning

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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Section: Aspects Of the Standard Wave Equationmentioning

confidence: 99%

“…[8][9][10][11] Here, we will use "soliton" as a shorthand for nonlinear, supersonic waves which preserve their shape, possibly with variations in amplitude, as they propagate. However, it must be borne in mind that the experimental evidence for this important property is difficult to assess and not fully convincing.…”

Section: Introductionmentioning

confidence: 99%

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

Verheest

Hellberg

2016

Physics of Plasmas

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“…Most of the studies carried out so far on ion-acoustic waves were confined to the unbounded planar geometry, although recently some works have been published in which cylindrical and spherical ion-acoustic waves have been discussed [45][46][47][48][49]. It may be mentioned that cylindrical and spherical symmetric solitons have been observed in plasma [50][51][52]. However, in these studies electrons were assumed to be isothermal.…”

Section: Introductionmentioning

confidence: 99%

Nonplanar ion-acoustic solitary waves in electron–positron–ion plasmas with electrons following aq-nonextensive distribution

2011

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Cylindrical and spherical Korteweg-de Vries equations were derived for ion-acoustic solitary waves in an unmagnetized three species plasma system comprised of cold ions, nonextensive electrons and thermal positrons by using standard reductive perturbation methods. The effects of nonplanar geometry and q-nonextensive electrons on the profiles of the amplitudes and widths of solitary structures were examined numerically.

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“…Indeed, there have been several experimental observations of cylindrical or spherical solitons. [8][9][10][11] Here, we will use "soliton" as a shorthand for solitary waves which preserve their shape, possibly with variations in amplitude, as they propagate. Rather recently, in the vast literature devoted to nonlinear electrostatic plasma modes, there have been theoretical efforts to break through the plane wave restriction and investigate nonplanar structures, which could be viewed as cylindrical or spherical equivalents of the well known modes.…”

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confidence: 99%