Field observation of soliton gases in the deep open ocean

Sander Wahls; Yu-Chen Lee

REVIEW 3 major objections 6 minor 34 references

Field observation of soliton gases in the deep open ocean

T0 review · 3 major / 6 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read Three deep-ocean sea states in Taiwan waters are confirmed as soliton gases, the first such open-ocean field evidence.

desk verdict A plausible first open-ocean soliton-gas detection, but the load-bearing directional-interference correction leans on unpublished work and an unvalidated random-phase assumption. read the letter →

arxiv 2510.04662 v2 pith:YX3WJJU3 submitted 2025-10-06 nlin.PS nlin.SIphysics.ao-phphysics.data-an

Yu-Chen Lee , Sander Wahls This is my paper · ORCID

classification nlin.PSnlin.SIphysics.ao-phphysics.data-an MSC 37K1576B1535Q55

keywords solitongasnonlinearFouriertransformNLSequationoceanwavesdirectionalinterferenceenergyratioEluanbibuoyBenjamin-FeirIndex

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

The paper claims the first field observation of soliton gases in the open ocean. Using the nonlinear Fourier transform to split measured wave time series into soliton and radiation parts, it identifies eleven sea states in Taiwan waters with soliton energy ratios above 0.9. Because directional spreading can inflate that ratio, the authors remove directional interference by reconstructing wave fields with random phases; three records from the Eluanbi station stay above the 0.5 dominance threshold. These three are presented as genuine NLS-type envelope soliton gases, occurring in only about 0.054% of qualified records.

What carries the argument

The central tool is the soliton energy ratio from the nonlinear Fourier transform (NFT) for the focusing nonlinear Schrödinger equation, which splits a wave field's energy into discrete soliton components and continuous radiation via a nonlinear Parseval formula. The corroborating device is a probabilistic directional filter: since only directional spectrum magnitudes are known, phases are drawn uniformly at random 100 times, and the directional spectrum is truncated to retention angles of 36 and 20 degrees to estimate how soliton energy ratios respond to removing directional interference.

What would settle it

For one of the three Eluanbi events, obtain phase-resolved directional wave data (from a stereo camera or a dense wave array) and compute the soliton energy ratio after truncating directional sidebands at 36 and 20 degrees using the true phases; if the ratio falls below 0.5, the confirmed-soliton-gas claim fails.

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Extended reading notes

Core claim

On its own terms, the paper establishes that three 20-minute wave records from the Eluanbi buoy, in 40 m water off southern Taiwan, are dominated by envelope solitons rather than linear dispersive radiation. The nonlinear Fourier transform of the example record shows 64 solitons and a soliton energy ratio of 0.96; inverse-transforming only the discrete soliton spectrum reproduces the measured elevation closely. After numerically removing directional sidebands with retention angles of 36 and 20 degrees, the three Eluanbi cases keep soliton energy ratios above 0.5 across 100 random-phase realisations. These rare states share short peak periods, modest wave heights, extreme steepness, and high

Load-bearing premise

The analysis assumes the true phases of the measured wave components are statistically equivalent to uniformly random phases, so that simulated random-phase distributions predict how the actual record's soliton ratio responds to directional filtering.

Editorial extensions

If this is right

Open-ocean soliton gases exist as measurable sea states, not just laboratory or lagoon phenomena.
Such states are extremely rare, roughly 0.054% of the 20,523 unimodal deep-water records examined.
High soliton energy ratios can be inflated by directional interference, so single-point time-series estimates need a directional correction before being called soliton gases.
The three Eluanbi states offer natural test beds for NLS soliton gas kinetic theory in the ocean.

Reading between the lines

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

If the random-phase assumption holds, other historical buoy archives with directional spectra could be re-screened, potentially finding more open-ocean soliton gas events.
Phase-resolved measurements (e.g., stereo video or wave arrays) of similar sea states could test whether real phases behave like random phases, going beyond this paper's probabilistic approach.
Because the identified states have low abnormality index and near-zero skewness, soliton gas dominance does not appear to coincide with rogue wave activity—an implication the data support but the paper does not foreground.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The genuinely new thing here is the claim: three deep-water buoy records from Taiwan with NFT soliton energy ratios that stay above 0.5 after a directional-interference correction, which the authors interpret as the first open-ocean soliton gases. The field observation is new relative to prior lagoon and flume work, and the paper is honest about the rarity (0.054%) and about the eight cases that remain uncertain after filtering. The internal logic is mostly consistent: the NFT computation is formal, the 0.9 initial threshold and the 0.5 post-filter threshold are explicit selection rules, and Fig. 2 shows a sensible reconstruction of the time series from the discrete spectrum for one case. That is real work and deserves credit.

The soft spots are real but not all equally soft. The biggest one is the random-phase reconstruction. The paper admits only spectral magnitudes are available, so they synthesize fields with uniformly random phases and assume those phases are statistically irrelevant to the post-filter soliton energy ratio. That assumption is exactly the one you would worry about for sea states selected for extreme steepness and high BFI: nonlinear phase coupling and bound harmonics could in principle change the post-filter ratio. I would have liked a surrogate check—bispectrum, skewness, or a comparison with the measured higher-order statistics—before accepting that the Eluanbi cases "are indeed soliton gases." The reader's stress test is fair on this point, though it is a conditional concern, not a demonstrated flaw.

Second, the claim that directional interference overestimates the soliton energy ratio rests on the authors' own submitted manuscript [33]. That is not fatal by itself, but it makes the central confirmation depend on an inaccessible result. The threshold drop from 0.9 to 0.5 also needs a sentence of justification; it is reasonable that a different criterion applies after filtering, but the paper does not say why 0.5 is the right cutoff for "soliton dominance."

Minor points: no data or code are released, which limits reproducibility; and the three accepted cases all come from one station, so the open-ocean claim is empirically narrow even if arithmetically correct.

On balance, I disagree with any reading that treats this as a fabricated or incoherent result. The analysis is transparent about its uncertainties and the statistical evidence for the three Eluanbi records is internally consistent. But the central claim is not yet established at the level the abstract implies. The paper deserves a serious referee: it is important enough, and the method is novel enough, that referees should examine the random-phase assumption, the unpublished [33], and the threshold semantics rather than have the paper desk-rejected. I would probably not cite the "first open-ocean observation" as fact yet, but I would cite the method if it survives peer review.

Referee Report

3 major / 6 minor

Summary. The paper analyzes 20,523 directional buoy records from three stations in Taiwan waters (Eluanbi, Gueishandao, Xiaoliuqiu) and applies the NLS nonlinear Fourier transform (NFT) to compute a soliton energy ratio E_sol/E_total for each record after imposing unimodal-spectrum and deep-water criteria. Eleven records are found with ratios ≥0.9; these are characterized by small wave heights, short peak periods, high steepness (>0.029) and high BFI (>0.31). Because directional interference may artificially raise the ratio, the authors synthesize surrogate wave fields from the measured directional spectrum magnitudes using uniformly random phases, filter the directional energy to retention angles Δθ=36° and 20°, and recompute the soliton energy ratio for 100 phase realizations per case. They report that the three Eluanbi records (cases 1–3) remain entirely above a 0.5 threshold after filtering, and conclude that these are soliton gas sea states, claimed as the first open-ocean observation of soliton gases. The remaining eight cases are treated as ambiguous because their distributions cross 0.5.

Significance. If the central claim holds, this is a valuable and novel observation: it would extend soliton-gas phenomenology from flume experiments and lagoons to the deep open ocean, with quantitatively characterized sea states and an extremely low occurrence rate (~0.05%). The use of the NFT with an explicit energy decomposition (E_total = E_sol + E_rad) and the disclosure of distributions via violin plots are strengths; the paper does not fit parameters to produce the eleven candidates, and the selection criteria are stated explicitly. However, the confirmation of the three Eluanbi cases depends on two load-bearing assumptions: (i) that random-phase surrogates preserve the statistical structure relevant to soliton content, and (ii) that the threshold of 0.5 is a physically meaningful criterion for soliton dominance. Both need substantial support before the 'indeed soliton gases' conclusion is accepted.

major comments (3)

[Directional filtering method, p. 4-5 and Fig. 4] The random-phase reconstruction assumes that the true Fourier phases of the measured records are statistically independent and uniformly distributed. The eleven candidate sea states are selected precisely for extreme nonlinearity (steepness >0.029, BFI >0.31, as shown in Fig. 3D,H,L), a regime where nonlinear interactions and bound harmonics can generate phase correlations. The paper provides no validation that the 100 random-phase realizations reproduce the higher-order statistics of the measured records (e.g., skewness, kurtosis, bispectrum, or phase coherence). Without such a check, the assertion that cases 1–3 'stay completely above the threshold of 0.5' after directional interference is removed does not follow from the data. I recommend adding a comparison of the measured records' bispectra or third-order statistics against the surrogate ensemble, and/or testing phase-correlated ini
[Selection thresholds, main text after Fig. 4] The initial identification of soliton-gas candidates uses a soliton energy ratio of at least 0.9 ('very high soliton energy ratio'), but after directional filtering the confirmation criterion drops to 0.5, described only as 'above which solitons are dominating.' No physical or literature-based justification is given for 0.5, and it is inconsistent with the paper's own emphasis on 'extremely high' ratios. Since cases 1–3 would not meet the 0.9 bar after filtering (their distributions, as shown in Fig. 4, appear centered near or below 0.9), the conclusion that they are 'indeed soliton gases' relies on this ad hoc threshold. Please justify the 0.5 threshold using NLS soliton-gas theory, numerical experiments, or prior observational studies, or rephrase the claim to reflect the weaker criterion.
[Reference [33] and the overestimation mechanism] The directional-filtering correction is motivated by the claim, attributed to the submitted manuscript [33], that NFT soliton energy ratios computed from time series 'typically overestimate the soliton content in the main propagation direction due to directional interference.' This is the central premise of the correction, but the manuscript is unpublished and not accessible to the reader. The paper should either provide the essential evidence for this overestimation in the Supplemental Material or replace the citation with published work. As it stands, the validity of the probabilistic filtering method cannot be independently assessed, and the three 'confirmed' cases rest on this unverified mechanism.

minor comments (6)

[Abstract and text] Typo: 'sol ion gas' appears in the abstract ('required for a sol ion gas has not been demonstrated') and a similar typo appears in the introduction ('for a solion gas'). Should be 'soliton gas'.
[Table I] The station name 'Elaunbi' is a misspelling of 'Eluanbi'.
[Fig. 3] The y-axis labels in panels (B), (F), (J) read '1.5 [rad]' but presumably denote directional spreading σθ in radians; the axis label is missing the symbol. Please fix.
[Fig. 2A] The label 'CgA' appears unexplained in the figure panel; if it denotes group velocity times amplitude or a soliton parameter, please clarify in the caption.
[Main text, p. 4] Typo: 'JONSW AP' should be 'JONSWAP'.
[Reference [5]] Author name 'A. El Gennady' appears incorrect; the correct author is G. A. El. Please verify all reference entries.

Circularity Check

2 steps flagged · score 4.0 of 10

Partial circularity: the directional-interference correction is justified by an unpublished self-citation, and the final 'soliton gas' confirmation applies the same ratio threshold used to indicate the class; the NFT/data analysis itself is independent.

self citation load bearing [Section 'Integrable models like the KdV or NLS equation…' (p. 3); reference [33]]
"In simulations of directional JONSWAP wave fields, the soliton energy ratio computed directly from time series was found to typically overestimate the soliton content in the main propagation direction due to directional interference, although the effect was less pronounced for strongly nonlinear sea states [33]."

This is the sole support for the premise that the measured NFT ratios must be discounted for directional interference. Reference [33] is the authors' own submitted manuscript (Y.-C. Lee and S. Wahls, submitted 2025), not an external or machine-checked result. The final conclusion that only cases 1–3 are soliton gases is produced by applying a correction whose necessity is imported from this self-citation. Because the correction changes an 11-case catalogue into a 3-case confirmation, this self-citation is load-bearing rather than incidental.
self definitional [Results, 'Soliton gases are thus indicated…' (p. 3) and Fig. 4 paragraph (p. 5)]
"Soliton gases are thus indicated by high soliton energy ratios. ... For the cases 1 to 3 (Eluanbi station), the distributions stay completely above the threshold of 0.5, above which solitons are dominating. We can thus consider them soliton gases even with directional interference taken into account."

The quantity used to indicate a soliton gas—the soliton energy ratio exceeding a threshold—is exactly the quantity measured and then presented as confirmation. Thus 'these records are soliton gases' is a restatement of 'their soliton energy ratio exceeds 0.5' rather than an independent test of the physical soliton-gas claim. The initial screening threshold 0.9 is also later replaced by 0.5 in the confirmation step, further tightening the definitional loop.

full rationale

The paper's core observation—11 out of 20,523 measured buoy records have NFT soliton energy ratios at or above 0.9—is a direct data analysis; the NFT and nonlinear Parseval relation are standard mathematical tools, so there is no circularity in computing the ratio. The directional-filtering step is not a fit to the target conclusion: random-phase realizations are generated from measured directional spectra and the post-filter ratios are genuinely simulated. However, the reason to distrust the raw ratios and apply filtering is taken from [33], an unpublished submission by the same authors, so the reduction from 11 candidates to 3 confirmations leans on a self-citation. In addition, the final 'confirming that they are indeed soliton gases' applies the same ratio-threshold indicator used to define/indicate soliton gases; it is therefore partly definitional. The paper honestly states the probabilistic nature of the filtering and that no definite answer can be given for cases 4–11. Overall, this is partial circularity, not a derivation that reduces entirely to its inputs.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new entities, forces, or conserved quantities. Its burden lies in assumptions about the validity of NLS-NFT for ocean waves, the random-phase directional filtering model, and the chosen thresholds. The central observational claim depends on these domain assumptions rather than on fitted parameters.

free parameters (4)

Candidate threshold for very high soliton energy ratio = 0.9
Events with NFT soliton energy ratio at least 0.9 are selected as candidates; this threshold determines the 11 identified cases and the 0.054% occurrence rate.
Post-filter soliton dominance threshold = 0.5
After directional filtering, a sea state is called a soliton gas if the simulated soliton energy ratio remains above 0.5; this relaxed threshold is used for the final claim.
Directional retention angles = 36° and 20°
Angular windows used to remove directional interference; chosen with reference to Slunyaev [34] but not derived; results vary with this choice.
Number of random phase realizations = 100
100 random phase sets per record are used to estimate distributions; the width and tails of the violin plots depend on this sample size.

assumptions (5)

domain assumption The NLS equation approximately describes deep-water wave envelopes, so NLS-NFT soliton/radiation decomposition is physically meaningful for the measured records.
Central to computing soliton energy ratios; the paper acknowledges integrable models approximate real ocean waves.
standard math The nonlinear Parseval relation decomposes normalized envelope energy into soliton and radiation parts.
From Ablowitz & Segur [30]; accepted result used without proof.
domain assumption Directional interference artificially increases the soliton energy ratio estimated from time series, and angular filtering with random phases removes this artifact.
Key to interpreting post-filter ratios; relies on the authors' submitted work [33].
domain assumption A soliton energy ratio above 0.5 means solitons dominate the wave field.
Definitional threshold used for the final conclusion; not derived from wave physics.
domain assumption Unimodal spectra and deep-water conditions select sea states where a single wind system and NLS dynamics apply.
Data selection criteria; suppresses crossing seas and broad spectral bandwidth.

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Cite this review

Pith. "Pith review of Field observation of soliton gases in the deep open ocean." pith.science (2026). https://pith.science/paper/YX3WJJU3

@misc{pith2026251004662,
  author       = {Pith},
  title        = {Pith review of: Field observation of soliton gases in the deep open ocean},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YX3WJJU3}},
  note         = {Machine review of arXiv:2510.04662}
}

read the original abstract

Soliton gases are large ensembles of random solitons with distinct characteristics arising from integrable system dynamics. They have been widely studied in theory and experiments, and were observed in natural lagoons. However, it remains an open question whether they occur naturally in the open ocean. Nonlinear ocean states containing solitons have been observed in the literature, but the dominance of solitons over other wave components required for a soliton gas has not been demonstrated. Our study provides the first field evidence of soliton gas sea states in the deep ocean, measured in Taiwan waters. The soliton energy ratio derived from the nonlinear Fourier transform (NFT) is used as a key parameter to quantify how close sea states are to soliton gases. We identify eleven measurements with extremely high soliton energy ratios. They are characterized by short-period waves with relatively small wave heights, accompanied by extreme steepness and Benjamin Feir Index (BFI) values. These states are exceptionally rare, representing only 0.054\% of our dataset. Since directional interference can artificially increase the estimated soliton energy ratio obtained from measured time series, we further apply a probabilistic directional filtering method to remove the directional interference. Three wave records from the Eluanbi station are found to retain high soliton energy ratios after the directional interference has been removed, confirming that they are indeed soliton gases.

Figures

Figures reproduced from arXiv: 2510.04662 by the authors.

**Figure 1.** FIG. 1. Data collection from buoy measurements in Taiwanese waters. (A) Locations of three buoy stations, Eluanbi (south), [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** FIG. 2. NFT analysis of a sea state with high soliton energy ratio. (A) Soliton spectrum. (B) Corresponding initial surface [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. Statistical properties of seas states with high soliton energy ratios of at least 0 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4. Investigation of reduced directional effects on field-measured soliton gases: distribution of soliton energy ratios for the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.

[1] [33]

Lee and S

Y.-C. Lee and S. Wahls, submitted (2025)

2025

[2] [1]

Camassa, J

R. Camassa, J. M. Hyman, and B. P. Luce, Physica D: Nonlinear Phenomena123, 1 (1998)

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[3] [2]

Y. S. Kivshar, Physical Review B43, 3493 (1991)

1991

[4] [3]

Manukure and T

S. Manukure and T. Booker, Partial Differential Equa- tions in Applied Mathematics4, 100140 (2021)

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Zakharov, Sov

V. Zakharov, Sov. Phys. JETP33, 538 (1971). 6

1971

[6] [5]

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A. El Gennady, Journal of Statistical Mechanics: Theory and Experiment2021, 114001 (2021)

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Suret, S

P. Suret, S. Randoux, A. Gelash, D. Agafontsev, B. Doyon, and G. El, Physical Review E109, 061001 (2024)

2024

[8] [7]

Onorato, A

M. Onorato, A. R. Osborne, M. Serio, L. Cavaleri, C. Brandini, and C. T. Stansberg, Phys. Rev. E70, 067302 (2004)

2004