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arxiv: 1907.11522 · v1 · pith:F5Y6KGLLnew · submitted 2019-07-25 · ⚛️ physics.plasm-ph

Dust-acoustic envelope solitons and rogue waves in an electron depleted plasma

J. Akter , N. A. Chowdhury , A. A. Mamun This is my paper

Pith reviewed 2026-05-24 16:07 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph
keywords dust acoustic wavesenvelope solitonsrogue wavesmodulational instabilityelectron-depleted plasmanon-extensive ionsdusty plasmaopposite polarity dust
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The pith

Dust acoustic waves in electron-depleted dusty plasmas form bright and dark envelope solitons as well as first- and second-order rogue waves.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors derive a nonlinear Schrödinger equation for the envelope dynamics of dust acoustic waves propagating in an unmagnetized plasma that contains warm dust grains of both signs and non-extensive positive ions but no electrons. They identify two distinct modes (fast and slow) and obtain explicit criteria separating regions where the waves remain stable from regions where they break into bright or dark envelope solitons and into first- or second-order rogue waves. The same analysis shows that dust mass, charge, and number densities, together with the ion non-extensivity parameter, shift the boundaries of modulational instability. A reader would care because these structures are proposed to occur in observed space plasmas such as Jupiter’s magnetosphere, Saturn’s F-ring, and cometary tails.

Core claim

Application of the reductive perturbation method to the fluid equations yields a nonlinear Schrödinger equation whose coefficients depend on the dusty-plasma parameters. Sign changes in the dispersion and nonlinearity coefficients delineate the existence domains of bright and dark envelope solitons; the same equation admits Peregrine-type solutions that constitute first- and second-order rogue waves. Both the modulational instability threshold and the soliton/rogue-wave profiles are shown to vary systematically with dust mass, dust charge, dust and ion densities, and the ion non-extensivity index.

What carries the argument

The nonlinear Schrödinger equation obtained via reductive perturbation from the warm-dust fluid equations coupled to non-extensive ion response.

If this is right

  • Dust mass, charge, and number densities shift the modulational instability threshold and the resulting soliton and rogue-wave profiles.
  • Both fast and slow dust-acoustic modes support bright and dark envelope solitons under appropriate parameter choices.
  • First- and second-order rogue waves appear when the carrier wave lies inside the modulational instability band.
  • The same dusty-plasma parameters that control instability also determine the amplitude and width of the localized structures.
  • The structures are expected in regions such as Jupiter’s magnetosphere, the upper mesosphere, Saturn’s F-ring, and cometary tails.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Laboratory dusty-plasma devices could test the predicted dependence of rogue-wave occurrence on dust charge sign and magnitude.
  • The non-extensive ion response used here could be replaced by other non-Maxwellian distributions to check robustness of the soliton criteria.
  • Extension of the same reductive-perturbation procedure to weakly magnetized geometries would reveal whether the rogue-wave existence domains survive the addition of gyromotion.
  • The parameter ranges identified could serve as initial conditions for particle-in-cell simulations that relax the fluid approximation.

Load-bearing premise

The reductive perturbation expansion remains uniformly valid throughout the parameter regime in which the modulational instability is predicted.

What would settle it

A laboratory or spacecraft measurement that records dust-acoustic wave envelopes remaining modulationally stable in a plasma whose measured dust charge, mass ratio, and ion non-extensivity parameter lie inside the paper’s predicted unstable domain would falsify the derived criteria.

Figures

Figures reproduced from arXiv: 1907.11522 by A. A. Mamun, J. Akter, N. A. Chowdhury.

Figure 1
Figure 1. Figure 1: Plot of P/Q vs k for different values of e3 when e1 = 0.07, e2 = 0.007, e4 = 2.0, q = 2, and ωs . where k and ω are real variables representing the carrier wave number and frequency, respectively. The derivative operators in the above equations are treated as follows: ∂ ∂t → ∂ ∂t − ǫvg ∂ ∂ξ + ǫ 2 ∂ ∂τ, (15) ∂ ∂x → ∂ ∂x + ǫ ∂ ∂ξ . (16) Now, by substituting (8)-(16) into (1)-(4), and (7), and equating the co… view at source ↗
Figure 4
Figure 4. Figure 4: Plot of Re(Φ) vs ξ for bright envelope soliton when e1 = 0.07, e2 = 0.007, e3 = 0.6, e4 = 2.0, q = 2, τ = 0, ψ0 = 0.002, U = 0.4, Ω0 = 0.4, k = 0.5, and ωf [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: Plot of P/Q vs k for different values of e3 when e1 = 0.07, e2 = 0.007, e4 = 2.0, q = 2, and ωf . It may be noted here that both P and Q are function of various plasma parameters such as q, e1, e2, e3, e4 and k. So, all the plasma parameters are used to maintain the nonlinearity and the dispersion properties of the EDDP medium. 4. Modulational instability The stable and unstable parametric regimes of the D… view at source ↗
Figure 6
Figure 6. Figure 6: Plot of |Φ| vs ξ for different values of e4 when e1 = 0.07, e2 = 0.007, e3 = 0.6, q = 2, τ = 0, ψ0 = 0.002, U = 0.4, Ω0 = 0.4, k = 0.5, and ωf . e4=1.5 e4=2.0 e4=2.5 -20 -10 0 10 20 0.00 0.01 0.02 0.03 0.04 Ξ F¤ [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Plot of |Φ| vs ξ for different values of e4 when e1 = 0.07, e2 = 0.007, e3 = 0.6, q = 2, τ = 0, ψ0 = 0.002, U = 0.4, Ω0 = 0.4, k = 0.1, and ωf . 5. Envelope solitons The bright and dark envelope solitons can be written as [36, 37, 38, 39] Φ(ξ, τ) =  ψ0 sech2  ξ − Uτ W  1 2 × exp " i 2P ( Uξ + [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: Plot of |Φ1| vs ξ for different values of q when e1 = 0.07, e2 = 0.007, e3 = 0.6, e4 = 2.0, τ = 0, k = 0.5, and ωf . (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p007_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: Plot of |Φ1| vs ξ for different values of q when e1 = 0.07, e2 = 0.007, e3 = 0.6, e4 = 2.0, τ = 0, k = 0.5, and ωf . The solutions (45) and (46) represent the profile of the first￾order and second-order RWs, which concentrate a significant amount of energy into a relatively small area, within the mod￾ulationally unstable parametric regime. We have numerically analyzed Eq. (45) in Figs. 8-10 to understand t… view at source ↗
Figure 11
Figure 11. Figure 11: Profile of the (a) first-order rational solution; ( [PITH_FULL_IMAGE:figures/full_fig_p007_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Profile of the first-order (dashed green curve) and [PITH_FULL_IMAGE:figures/full_fig_p008_12.png] view at source ↗
read the original abstract

Theoretical investigation of the nonlinear propagation and modulational instability (MI) of the dust acoustic (DA) waves (DAWs) in an unmagnetized electron depleted dusty plasma (containing opposite polarity warm dust grains and non-extensive positive ions) has been made by deriving a nonlinear Schr\"{o}dinger equation with the help of perturbation method. Two types of mode, namely, fast and slow DA modes, have been found. The criteria for the formation of bright and dark envelope solitons as well as the first-order and second-order rogue waves have been observed. The effects of various dusty plasma parameters (viz., dust mass, dust charge, dust and ion number densities, etc.) on the MI of DAWs have been identified. It is found that these dusty plasma parameters significantly modify the basic features of the DAWs. The applications of the results obtained from this theoretical investigation in different regions of space, viz., magnetosphere of Jupiter, upper mesosphere, Saturn's F-ring, and cometary tail, etc.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript derives a nonlinear Schrödinger equation (NLSE) via the reductive perturbation method for dust-acoustic waves in an unmagnetized electron-depleted plasma containing opposite-polarity warm dust grains and non-extensive ions. It identifies fast and slow modes and determines existence criteria for bright/dark envelope solitons and first-/second-order rogue waves from the signs of the NLSE coefficients, while mapping the effects of dust mass, charge, densities, and the non-extensivity parameter q on modulational instability, with applications suggested for space plasmas such as Jupiter's magnetosphere and cometary tails.

Significance. If the NLSE coefficients are correctly obtained and the small-amplitude ordering remains consistent, the parameter maps for soliton and rogue-wave regimes would offer a useful extension of envelope-soliton theory to electron-depleted dusty plasmas. The explicit identification of fast/slow modes and q-dependent MI boundaries could aid interpretation of nonlinear structures in the cited space environments.

major comments (2)
  1. [NLSE derivation and MI analysis] The central claim that bright/dark envelope solitons and rogue waves form according to the signs of the NLSE coefficients rests on the reductive-perturbation derivation remaining valid throughout the quoted ranges of dust mass, charge, and q; no estimate of the size of neglected higher-order terms or comparison against a kinetic dispersion relation is supplied to confirm this ordering (see the section deriving the NLSE and the subsequent MI analysis).
  2. [Plasma model and coefficient evaluation] The non-extensive ion distribution is adopted without any consistency check against the electron-depleted, warm-dust closure for the modulation wave numbers where MI is reported; if the q-distribution fails to capture the ion kinetics inside those regimes, the reported sign changes in P and Q (and therefore the soliton/rogue-wave boundaries) shift or vanish.
minor comments (2)
  1. [Abstract] The abstract states that 'the criteria ... have been observed' but the manuscript is purely theoretical; rephrase to 'determined' or 'obtained'.
  2. [Figures] Figure captions and axis labels should explicitly state the fixed values of q, dust charge, and density ratios used when plotting the MI growth rate or soliton profiles.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [NLSE derivation and MI analysis] The central claim that bright/dark envelope solitons and rogue waves form according to the signs of the NLSE coefficients rests on the reductive-perturbation derivation remaining valid throughout the quoted ranges of dust mass, charge, and q; no estimate of the size of neglected higher-order terms or comparison against a kinetic dispersion relation is supplied to confirm this ordering (see the section deriving the NLSE and the subsequent MI analysis).

    Authors: We agree that an explicit estimate of the size of neglected higher-order terms would strengthen the justification for the validity of the reductive perturbation method over the quoted parameter ranges. In a revised manuscript we will add a short discussion paragraph that estimates the magnitude of the leading neglected terms under the small-amplitude ordering for representative values of dust mass, charge and q. A direct numerical comparison against a kinetic dispersion relation lies outside the scope of the present fluid model and is not feasible within the current study. revision: partial

  2. Referee: [Plasma model and coefficient evaluation] The non-extensive ion distribution is adopted without any consistency check against the electron-depleted, warm-dust closure for the modulation wave numbers where MI is reported; if the q-distribution fails to capture the ion kinetics inside those regimes, the reported sign changes in P and Q (and therefore the soliton/rogue-wave boundaries) shift or vanish.

    Authors: The non-extensive ion distribution is introduced as a standard phenomenological model for non-Maxwellian ions in the cited space-plasma environments and is applied consistently with the fluid closure for the warm dust grains under the electron-depleted assumption. The NLSE coefficients (and therefore the signs of P and Q) are derived directly from this closed set of equations; no additional kinetic closure is imposed. Within the adopted model the reported boundaries remain valid. An explicit kinetic consistency check for the modulation wave numbers would require a separate kinetic treatment that is not part of the present work. revision: no

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives the NLSE via reductive perturbation from the fluid equations incorporating non-extensive ions and warm dust, then determines soliton/rogue-wave criteria from the signs of the resulting P and Q coefficients. This is a standard forward analytical chain with no self-definitional reduction, no fitted parameters renamed as predictions, and no load-bearing self-citations or ansatzes imported from prior author work. The existence conditions follow directly as consequences of the derived coefficients evaluated at input plasma parameters, without tautology or statistical forcing.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 0 invented entities

The central claim rests on the validity of the reductive perturbation expansion and the modeling choice of non-extensive ion statistics; no free parameters are explicitly fitted in the abstract, but the non-extensivity index functions as an adjustable model parameter.

free parameters (1)
  • non-extensivity parameter q
    Index in the ion distribution function; chosen to represent deviation from Maxwellian statistics.
axioms (3)
  • domain assumption Plasma is unmagnetized and electron depleted
    Core modeling assumption stated in the abstract.
  • domain assumption Dust grains are warm and carry opposite polarity charges
    Defines the plasma composition used throughout the derivation.
  • domain assumption Ions obey non-extensive (Tsallis) statistics
    Replaces Maxwellian distribution in the fluid equations.

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discussion (0)

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Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    Sahu and M

    B. Sahu and M. Tribeche, Astrophys. Space Sci. 338, 259 (2012)

    work page 2012

  2. [2]

    M. M. Hossen, et al., Phys. Plasmas 23, 023703 (2016)

    work page 2016

  3. [3]

    M. M. Hossen, et al., Eur. Phys. J. D 70, 252 (2016)

    work page 2016

  4. [4]

    S. K. Zaghbeer, et al., Astrophys. Space Sci. 353, 493 (2014)

    work page 2014

  5. [5]

    M. M. Hossen, et al., High Energy Density Phys. 24, 9 (2017)

    work page 2017

  6. [6]

    Jahan, et al., Commun

    S. Jahan, et al., Commun. Theor. Phys. 71, 327 (2019)

    work page 2019

  7. [7]

    A. S. Bains, et al., Astrophys. Space Sci. 343, 621 (2013)

    work page 2013

  8. [8]

    Sahu and M

    B. Sahu and M. Tribeche, Astrophys. Space Sci. 341, 573 (2012)

    work page 2012

  9. [9]

    Shahmansouri and H

    M. Shahmansouri and H. Alinejad, Phys. Plasmas 20, 033704 (2013)

    work page 2013

  10. [10]

    P . K. Shukla and A. A. Mamun, Introduction to Dusty Plasma Physics (Institute of Physics, Bristol, 2002)

    work page 2002

  11. [11]

    Ferdousi, et al., Astrophys

    M. Ferdousi, et al., Astrophys. Space Sci. 43, 360 (2015)

    work page 2015

  12. [12]

    Emamuddin, et al., Phys

    M. Emamuddin, et al., Phys. Plasmas 20, 043705 (2013)

    work page 2013

  13. [13]

    Barkan, et al., Phys

    A. Barkan, et al., Phys. Plasmas 2, 3563 (1995)

    work page 1995

  14. [14]

    Ferdousi, et al., Eur

    M. Ferdousi, et al., Eur. Phys. J. D 71, 102 (2017)

    work page 2017

  15. [15]

    Eghbali, et al., Pramana J

    M. Eghbali, et al., Pramana J. Phys. 88, 15 (2017)

    work page 2017

  16. [16]

    N. N. Rao, et al., Planet. Space Sci. 38, 543 (1990)

    work page 1990

  17. [17]

    Renyi, Acta Math

    A. Renyi, Acta Math. Acad. Sci. Hung. 6, 285 (1955)

    work page 1955

  18. [18]

    Tsallis, J

    C. Tsallis, J. Stat. Phys. 52, 479 (1988)

    work page 1988

  19. [19]

    T. E. Eastman, et al., et. al., Geophys. Res. Lett. 103, 23503 (1998)

    work page 1998

  20. [20]

    G. P . Pavlos, et al., Physica A 390, 2819 (2011)

    work page 2011

  21. [21]

    M. H. Rahman, et al., Phys. Plasmas 25, 102118 (2018)

    work page 2018

  22. [22]

    Bacha, et al., Physica A 466, 199 (2017)

    M. Bacha, et al., Physica A 466, 199 (2017)

    work page 2017

  23. [23]

    Roy, et al., Astrophys

    K. Roy, et al., Astrophys. Space Sci. 350, 599 (2014)

    work page 2014

  24. [24]

    Bacha and M

    M. Bacha and M. Tribeche, Astrophys. Space Sci. 337, 253 (2012)

    work page 2012

  25. [25]

    S. A. El-Tantawy, et al., Astrophys. Space Sci. 337, 209 (2012)

    work page 2012

  26. [26]

    Borhanian et al., Phys

    J. Borhanian et al., Phys. Plasmas 20, 013707 (2013)

    work page 2013

  27. [27]

    Tribeche, et al., Phys

    M. Tribeche, et al., Phys. Plasmas 7, 4013 (2000)

    work page 2000

  28. [28]

    Tribeche, et al., Phys

    M. Tribeche, et al., Phys. Plasmas 11, 3001 (2004)

    work page 2004

  29. [29]

    Tadsen, et al., Phys

    B. Tadsen, et al., Phys. Plasmas 22, 113701 (2015)

    work page 2015

  30. [30]

    Steckiewicz, et al., et al., Geophys

    M. Steckiewicz, et al., et al., Geophys. Res. Lett. 42, 8877 (2015)

    work page 2015

  31. [31]

    P . K. Shukla and V . P . Silin, Phys. Scr.45, 508 (1992)

    work page 1992

  32. [32]

    S. G. Tagare, Phys. Plasmas 04, 3167 (1997)

    work page 1997

  33. [33]

    N. A. Chowdhury, et al., Phys. plasmas 24, 113701 (2017)

    work page 2017

  34. [34]

    M. H. Rahman, et al., Chinese J. Phys. 56, 2061 (2018)

    work page 2061

  35. [35]

    N. A. Chowdhury, et al., Contrib. Plasma Phys. 58, 870 (2018)

    work page 2018

  36. [36]

    Kourakis and P

    I. Kourakis and P . K. Shukla, Phys. Plasmas 10, 3459 (2003)

    work page 2003

  37. [37]

    Kourakis et al., Nonlinear Proc

    I. Kourakis et al., Nonlinear Proc. Geophys. 12, 407 (2005)

    work page 2005

  38. [38]

    N. A. Chowdhury, et al., V acuum147, 31 (2018)

    work page 2018

  39. [39]

    Fedele, Phys

    R. Fedele, Phys. Scr. 65, 502 (2002)

    work page 2002

  40. [40]

    W. M. Moslem, et al., Physical Review E 84, 066402 (2011)

    work page 2011

  41. [41]

    N. A. Chowdhury, et al., Plasma Phys. Rep. 45, 459 (2019)

    work page 2019

  42. [42]

    Ahmed, et al., Chaos 28, 123107 (2018)

    N. Ahmed, et al., Chaos 28, 123107 (2018)

    work page 2018

  43. [43]

    N. A. Chowdhury, et al., Chaos 27, 093105 (2017)

    work page 2017

  44. [44]

    R. E. Tolba, et al., Phys. Plasmas 22, 043707 (2015)

    work page 2015

  45. [45]

    T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967)

    work page 1967

  46. [46]

    A. M. Turing, Philos. Trans. R. Soc. London B 237, 37 (1952)

    work page 1952

  47. [47]

    Chabchoub, et al., Phys

    A. Chabchoub, et al., Phys. Rev. Lett. 106, 204502 (2011)

    work page 2011

  48. [48]

    Chabchoub, et al., Phys

    A. Chabchoub, et al., Phys. Rev. X 2, 011015 (2012)

    work page 2012

  49. [49]

    Bailung, et al., Phys

    H. Bailung, et al., Phys. Rev. Lett. 107, 255005 (2011)

    work page 2011

  50. [50]

    Kibler, et al., Nat

    B. Kibler, et al., Nat. Phys. 6, 790 (2010)

    work page 2010

  51. [51]

    Plasmas 22, 092124 (2015)

    Shalini, et al., Phys. Plasmas 22, 092124 (2015)

    work page 2015

  52. [52]

    Guo, et al., Ann

    S. Guo, et al., Ann. Phys. 332, 38 (2013)

    work page 2013

  53. [53]

    Ankiewicz, et al., J

    A. Ankiewicz, et al., J. Phys. A 43, 12002 (2010)

    work page 2010

  54. [54]

    Ankiewicz, et al., Phys

    A. Ankiewicz, et al., Phys. Lett. A 373, 3997 (2009). 8

    work page 2009