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REVIEW 3 major objections 6 minor 29 references

Action potentials and solitons

T0 review · 3 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The paper argues that action potentials and solitons are physically distinct: action potentials are threshold-driven active-medium waves, while solitons are conservative nonlinear-dispersive waves, and soliton formation from arbitrary excit

desk verdict A clear, honest review essay that restates the AP/soliton distinction with helpful simulations but overreaches in its timescale-based conclusion. read the letter →

arxiv 2607.20496 v1 pith:KHSPTSXI submitted 2026-06-15 physics.bio-ph

Jüri Engelbrecht , Kert Tamm , Tanel Peets This is my paper · ORCID
classification physics.bio-ph MSC 92C2035Q5135Q53
keywords actionpotentialsolitonsolitarywaveHodgkin-HuxleyBoussinesqequationHeimburg-Jacksonmodelnervesignalactivemedium
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to settle a terminological and conceptual dispute in neuroscience: whether the action potential can be described as a soliton. It argues that the two are different physical objects: an action potential is an active, threshold-driven solitary wave that annihilates on collision, whereas a soliton is a conservative, nonlinear-dispersive wave that passes through other solitons with only a phase shift. Using numerical examples from a Hodgkin-Huxley-type model and from Boussinesq-type equations (including the improved Heimburg-Jackson membrane model), it shows that soliton formation from an arbitrary initial pulse takes roughly 110 ms and meters of propagation, far exceeding the timescale of action potentials. The upshot is that the term 'soliton' should be reserved for its mathematical-physics meaning, and the accompanying mechanical wave in the membrane should be treated as a solitary wave, not the signal itself.

What carries the argument

The argument is carried by a contrast between two mathematical descriptions. On one side is the Hodgkin-Huxley paradigm, in particular the Lieberstein modification including inductance, whose equations contain an ion-current source term and a threshold: subthreshold inputs decay, superthreshold inputs produce the same action potential regardless of amplitude. On the other side is the Boussinesq paradigm, specifically the improved Heimburg-Jackson equation U_TT = C0^2 U_XX + P U U_XX + Q U^2 U_XX + P U_X^2 + 2Q U U_X^2 - H1 U_XXXX + H2 U_XXTT, a conservative equation with nonlinear and dispersive terms that supports analytic soliton solutions of the form U(xi) = 6(c^2 - C0^2)/P / (1 + sqrt(1

What would settle it

A direct experiment or simulation that produced a well-separated membrane soliton train from an initial pulse within less than a millisecond and a few centimeters using physiologically plausible membrane parameters would contradict the timescale argument. Alternatively, a head-on collision experiment in which two mechanical pulses in the membrane pass through each other unchanged, rather than annihilating, would weaken the claim that AP-like signals are not solitons, though it would not by itself settle the classification.

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Extended reading notes

Core claim

The central claim is that the physics of emergence of action potentials and solitons is fundamentally different. Action potentials are generated by voltage-gated ion channels in an active medium: an above-threshold stimulus triggers a stereotyped asymmetric pulse whose amplitude is independent of stimulus strength, and two counter-propagating action potentials annihilate each other. Solitons are solutions of conservative nonlinear dispersive equations like the KdV or Boussinesq equations, where the balance of nonlinearity and dispersion produces shape-preserving waves whose speed depends on amplitude and which survive collisions with only a phase shift. The paper demonstrates numerically tha

Load-bearing premise

The conclusion that solitons are irrelevant to nerve signals depends on the specific improved Heimburg-Jackson parameter set in which soliton formation takes about 110 ms and two meters; if other physiological parameter regimes or other Boussinesq-type models formed solitons on sub-millisecond timescales, the blanket dismissal would lose force.

Editorial extensions

If this is right

  • The term 'soliton' should not be used as a synonym for 'solitary wave'; an action potential is a solitary wave in an active medium, not a soliton.
  • Mechanical waves accompanying action potentials should be interpreted as solitary waves that may be driven by the action potential, rather than as the signal itself.
  • Models of nerve pulse propagation must incorporate the active ion mechanism to reproduce threshold behaviour and head-on annihilation; conservative Boussinesq-type equations alone do not generate a pulse on physiological timescales.
  • Collision experiments provide a sharp test: head-on action potentials annihilate, while membrane mechanical pulses pass through with phase shift; any model must match this distinction.
  • The terminology of mathematical physics matters for interpreting numerical results: a model supporting soliton solutions does not make the biological signal a soliton.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the ~110 ms / ~2 m soliton-formation timescale holds across physiologically plausible parameters, then in short axons the mechanical wave accompanying an AP is better viewed as a forced response to the AP rather than an independent propagating signal.
  • The comparison suggests a testable extension: systematic parameter sweeps of the iHJ/Boussinesq model under physiological constraints could map the region where soliton formation is fast enough to matter; if such a region exists, the blanket conclusion would need refinement.
  • The paper's reasoning implies that van der Waals type models, which capture annihilation on head-on collision, may be more appropriate for mechanical aspects of the AP than the original Heimburg-Jackson formulation, but the terminology point stands regardless of model choice.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This paper argues that action potentials (APs) and solitons are fundamentally different objects: APs are solitary waves in an active, dissipative medium generated by the Hodgkin–Huxley ion mechanism, whereas solitons are nonlinear waves in conservative dispersive media arising from a balance of nonlinearity and dispersion. The authors present definitions (Section 2), numerical examples of soliton-train formation from a microstructured-solid model and the improved Heimburg–Jackson (iHJ) model (Section 3), and examples from the Lieberstein (Hodgkin–Huxley-type) model for AP generation and collision. They conclude that the time scale for soliton emergence from an arbitrary initial excitation (~110 ms, ~2 m) exceeds that of typical APs, and that 'solitons are not appropriate for describing nerve signals.'

Significance. If the conclusions are accepted, the paper provides a useful terminological and conceptual clarification for neuroscience, distinguishing solitary waves from solitons in the strict mathematical-physics sense. The strength of the paper is its emphasis on the different generation mechanisms (active vs conservative) and interaction properties (annihilation vs elastic collision), supported by established references and reproducible numerical methods (pseudospectral scheme, parameters listed in the appendix). The paper is synthetic rather than novel in its derivations, which is appropriate for an essay. However, the quantitative claim about soliton emergence timescales and its use to rule out solitons in nerve signalling rests on a narrow parameter choice and is not yet supported by sensitivity analysis; this limits the force of the blanket conclusion.

major comments (3)
  1. [Section 3, Fig. 3; Abstract] The statement that soliton formation requires ~110 ms and ~2 m is based on a single simulation of the iHJ model with parameters P=−0.2186, Q=0.004230, H1=72.14, H2=1.000 (Fig. 3). The paper itself cautions (Section 3) that 'even before considering ... if all assumptions made during derivation ... are justified' and that other parameter combinations produce different behaviors (Fig. 4). Since the Abstract and Section 4 use this timescale to conclude that 'solitons are not appropriate for describing nerve signals,' the claim is load-bearing. A sensitivity analysis over the measured physiological parameter ranges and initial-condition space, or an explicit qualification that the conclusion is parameter-specific, is needed before the blanket statement can be accepted.
  2. [Section 4; Abstract] The comparison 'time-scale of emerging solitons ... exceeds the time-scale of the usual AP existence' is not quantitatively defined. The AP is shown in Fig. 6 over tens of milliseconds and centimeters, while the soliton train in Fig. 3 is computed in dimensionless time. The paper does not state whether 'AP existence' means the duration of the AP at a fixed point, the time for the AP to traverse a typical axon, or another metric. Without a definition and a direct comparison, the reader cannot evaluate the claim. Please specify a quantitative measure and, ideally, plot both processes on comparable axes.
  3. [Section 4, final paragraph] The final conclusion 'solitons are not appropriate for describing nerve signals' conflates two separate points: (i) APs and solitons are defined by different physical mechanisms, which is well argued; and (ii) the emergence timescale of solitons from a localised initial condition is too long to be relevant for APs, which depends on the specific model and parameters. The authors themselves note in Section 4 that van der Waals-type models [23,24] may capture AP-like phenomena better than the iHJ model. The conclusion should be separated into these components and the timescale argument qualified accordingly.
minor comments (6)
  1. [Abstract / Section 4] The phrase 'time-scale of the usual AP existence' is undefined; please specify the intended metric (e.g., AP duration at a point, propagation time over a typical axon) and give the numerical value used.
  2. [Section 3, paragraph after Fig. 3] 'typical dimensions of nerve axons' is vague; human axons can exceed 1 m in length, so a 2 m propagation distance is not obviously 'significantly more.' Clarify what is meant (e.g., typical axon length, AP wavelength, or conduction distance of interest).
  3. [Appendix, after eq. (6)] There is a typo: 'action potnetial' should be 'action potential.' Also, 'psuedospectral' appears in Section 3; should be 'pseudospectral.'
  4. [Fig. 7] The top and bottom panels have different units (space in cm vs dimensionless space, time in ms vs dimensionless time). To make the qualitative comparison clear, either use consistent variables or explicitly label the axes in each panel; the current figure may mislead readers comparing the two panels.
  5. [Section 2] The paper contrasts 'solitary wave' and 'soliton' but does not formally define 'solitary wave.' Consider adding a one-sentence definition to make the distinction precise.
  6. [References] References [8] and [9] are dated 2026 with volume numbers; if this is a preprint, please indicate the publication status or update the references.

Circularity Check

0 steps flagged · score 2.0 of 10

Synthesis grounded in external definitions and models; only mild self-citation, no construction-equivalent circularity.

full rationale

The paper is a conceptual review, not a derivation: it compares established definitions of action potentials (Hodgkin-Hxley [1], Lieberstein [6]) with established soliton theory (KdV [2], Boussinesq-type models). The central claim—APs are waves in an active medium with threshold dynamics, while solitons are conservative nonlinear-dispersive waves—is supported by external sources and direct numerical simulations, not by fitting a parameter and later calling it a prediction. The timescale argument in Section 3 and Fig. 3 (soliton train at T=98001, ~110 ms, ~2 m) is a concrete iHJ-model simulation with stated parameters; although the simulation comes from the authors' prior work [18,19], it is not invoked as a uniqueness theorem or as an ansatz, and the main claim about different emergence physics would stand independently on the HH/KdV comparison. The paper itself limits the quantitative assertion: 'Even before considering the question if all assumptions made during derivation, like taking a conservative system (no dissipation or energy inflow), are justified...' (Section 3), and explicitly shows parameter dependence and alternate behaviours (Fig. 4). No equation is defined in terms of the conclusion, no fitted quantity is renamed as a prediction, and no load-bearing step reduces to a self-citation chain. The self-citation pattern is mild and not circular, yielding score 2 rather than 0.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new entities; it re-uses existing models (HH, iHJ, MEP) from the literature.

free parameters (1)
  • iHJ model parameters for Fig. 3 = P=-0.2186, Q=0.004230, H1=72.14, H2=1.000
    Taken from [19]; the timescale claim (110 ms, 2 m) depends on these values, but they are not fitted in this paper.
assumptions (3)
  • domain assumption A soliton is defined by the KdV-type properties: shape preservation, amplitude-dependent velocity, elastic collision.
    The paper uses this definition (Section 2) to argue APs are not solitons; it is a choice of terminology, not a proven fact.
  • domain assumption The Hodgkin-Huxley model accurately describes AP generation in active nerve membranes.
    Invoked in Section 1 and 3 as the physiological baseline; the paper does not question it.
  • domain assumption The Boussinesq-type equation (2) describes longitudinal mechanical waves in biomembranes.
    Heimburg-Jackson [5] assumption, stated in Section 1; the paper builds its timescale argument on it.

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Cite this review

Pith. "Pith review of Action potentials and solitons." pith.science (2026). https://pith.science/paper/KHSPTSXI

@misc{pith2026260720496,
  author       = {Pith},
  title        = {Pith review of: Action potentials and solitons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KHSPTSXI}},
  note         = {Machine review of arXiv:2607.20496}
}
read the original abstract

During the last decade, the notion of solitons has been mentioned in neuroscience related to the propagation of action potentials (AP). In this paper, based on many studies in mathematical physics and neuroscience, the clear differences between the APs and solitons are summarised. It is stressed that the physics of the emergence of APs and solitons is fundamentally different. The numerical examples collected from earlier studies demonstrate the differences in the process of generation and interaction of corresponding waves explicitly. It is also noted that although the longitudinal mechanical waves in biomembranes can be described by the Boussinesq-type equation, the time-scale of emerging solitons from an arbitrary initial excitation exceeds the time-scale of the usual AP existence considerably.

Figures

Figures reproduced from arXiv: 2607.20496 by the authors.

Figure 1
Figure 1. Left panel – typical action potential (AP) (model eqs. (6) and (7) [8]). Right panel – soliton profile (see eq. (4) for analytical solution of improved Heimburg-Jackson model (2)) (see [18] for details). Here (in eq. (4)) 𝑋 is dimensionless space, 𝑇 is dimensionless time, 𝑐 is normalised (dimensionless) velocity, and 𝜉 represents a moving frame of reference propagating with the soliton-type solution. 0 0.5 1 1.5 2 2… view at source ↗
Figure 2
Figure 2. Formation of a soliton train in a Boussinesq-type equation from a localised initial disturbance. See [12] for details (model equation (1) with parameters 𝛿 = 0.09, 𝑏 = 0.7188, 𝛽 = 56.0, 𝛾 = 9.3867, 𝜇 = 1.1394, 𝜆 = 1.1470). Left panel: sech2 -type initial condition, 𝑈0 = 1, 𝐵0 = 0.01. Right panel: left-propagating train of solitons at 𝑇 = 15700. 0 0.5 1 1.5 2 2.5 Dimensionless space 104 0 0.5 1 1.5 2 Dimensionless am… view at source ↗
Figure 3
Figure 3. Improved Heimburg Jackson model (2), the formation of a soliton train from localised initial disturbance [19]. Left panel – initial profile. Right panel - the formed soliton train at 𝑇 = 98001. Parameters 𝑃 = −0.2186, 𝑄 = 0.004230, 𝐻1 = 72.14, 𝐻2 = 1.000 (see [19] for details). J.Engelbrecht, K.Tamm, T.Peets: Preprint submitted to Elsevier Page 4 of 9 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Improved Heimburg Jackson model (2), the formation of a soliton train from localised initial disturbance [18]. Left panel - initial profiles with amplitudes 1 and -1. Right panel – positive and negative amplitude soliton trains (depending on the polarity of the initial…
Figure 5
Figure 5. Figure 5: Formation of solitons from initial pulses with different widths and amplitudes for the iHJ equation. Parameters 𝑃 = −0.16, 𝑄 = 0.8, 𝐻1 = 2, 𝐻2 = 3. Space length 1024𝜋 (dimensionless) and spatial grid 𝑛 = 8192. Time 𝑇 = 2198 (dimensionless). Left - initial pulses (with …
Figure 6
Figure 6. Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Contour plots (isolines) demonstrating the interaction of solitary pulses (bottom panel, model eq. (2)) versus interaction of counter-propagating AP signals (top panel, model eqs. (6) and (7)). In both cases, periodic boundary conditions were used in space. Note how th…

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Works this paper leans on

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