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Nonlinear wave dynamics on a chip

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A 6.7-nm superfluid helium film on a silicon chip recreates extreme shallow-water wave dynamics: backward-leaning waves, shock fronts, and fission into twelve solitons.

desk verdict A genuinely new chip-scale superfluid wave flume with first direct time-resolved evidence of backward steepening and hot solitons, but the height calibration needs error bars before the quantitative claims are fully trusted. read the letter →

arxiv 2504.13001 v1 pith:SITHO7N4 submitted 2025-04-17 physics.flu-dyn physics.opticsquant-ph

Matthew T. Reeves , Walter W. Wasserman , Raymond A. Harrison , Igor Marinkovic , Nicole Luu , Andreas Sawadsky , Yasmine L. Sfendla , Glen I. Harris
show 2 more authors
Warwick P. Bowen Christopher G. Baker
This is my paper · ORCID
classification physics.flu-dynphysics.opticsquant-ph
keywords superfluidheliumfilmsthirdsoundshallowwaterwavessolitonfissiondispersiveshockoptomechanicsUrsellnumberKdVequation
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 claims that a 6.7-nm-thick superfluid helium film, self-assembled on a silicon photonic-crystal beam and driven by optomechanical fountain pressure, behaves as a wave flume with shallow-water nonlinearities far beyond terrestrial facilities: an Ursell number $\mathrm{Ur}=H\lambda^2/h^3$ near $4\times 10^8$, about five orders of magnitude above the largest full-scale flumes. Using the same optical cavity to launch the waves and to read out the film height, it reports direct, time-resolved observations of backward-leaning waves, near-discontinuous dispersive shock fronts, and fission of a large wave into a train of up to twelve solitons that travel as depressions, the long-predicted 'hot solitons' of third-sound waves, the superfluid analogue of shallow-water waves. A sympathetic reader would care because this turns a regime previously studied in hundred-metre flumes, or only imagined for superfluids, into a lithographically reconfigurable laboratory on a chip with millisecond measurement cycles.

What carries the argument

The load-bearing object is a femtolitre superfluid helium film, 6.7 nm thick, on a silicon photonic-crystal resonator that serves as wave maker and height gauge at once. Nonlinearity enters because the van der Waals acceleration replaces gravity: the third-sound speed $c_3\simeq 5.9$ m/s obeys $c_3=(3\alpha_{\mathrm{vdW}}/h^3)^{1/2}$, so the speed decreases with wave height and troughs outrun crests, producing the backward lean quantified by the Ursell number $\mathrm{Ur}=H\lambda^2/h^3$. The KdV equation $u_t+\alpha u u_x+\beta u_{xxx}=0$ is the organizing model used to interpret steepening, shock formation, and fission, while the photonic-crystal acoustic Bragg grating supplies the dominant normal dispersion; together these set the number of solitons and make them propagate as micrometer-scale depressions, the 'hot solitons'.

What would settle it

Measure a known film-thickness change by an independent technique, for example using the second optical resonance at 1524 nm with its different $G/2\pi$, and compare the inferred wave heights; if the heights and hence the Ursell number shift materially, the quantitative nonlinearity claim fails, even though the observed temporal asymmetries would stand.

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Extended reading notes

Core claim

The central claim is that nonlinear shallow-water dynamics long predicted for superfluid helium—backward wave steepening caused by an effective van der Waals gravity $g_{\mathrm{vdW}}=3\alpha_{\mathrm{vdW}}/h^4$ that decreases with height, dispersive shock fronts, and soliton fission—can be observed directly in a 6.7 nm film on a 100 $\mu$m silicon beam, in the form of third-sound waves, the superfluid analogue of shallow-water waves. The optomechanical cavity both drives the wave through the fountain effect and measures the film elevation, and the measured wave profiles match a custom Euler simulation and a KdV model. The paper further claims that the photonic-crystal holes act as an acoustic Bragg grating whose normal dispersion, roughly 35 times the hydrodynamic value, controls the number and depression-versus-peak character of the solitons, stabilizing micrometer-scale hot solitons.

Load-bearing premise

Everything quantitative about the nonlinearity—the roughly 3 nm wave height, the $4\times 10^8$ Ursell number, and the comparison with extreme terrestrial flows—rests on converting photodetector voltage to film height using a fitted Lorentzian response and a finite-element value $G/2\pi=5.6$ GHz/nm, with no independent measurement or stated uncertainty for that conversion.

Editorial extensions

If this is right

  • Shallow-water nonlinear phenomena—steepening, dispersive shocks, and soliton fission—can be studied in a lithographically defined chip with millisecond measurement cycles instead of hundred-metre flumes.
  • By scaling flume length, film thickness, and drive amplitude, the platform can cover roughly nine orders of magnitude in Ursell number, from $10^2$ to more than $10^{11}$.
  • Engineering the acoustic dispersion of the photonic crystal controls both the number of solitons emerging from fission and whether they appear as depressions or elevations.
  • The observations confirm the long-predicted hot-soliton regime in superfluid third sound, in which solitons are traveling depressions with locally increased temperature.

Reading between the lines

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

  • A natural extension not demonstrated here is a distributed array of height sensors along the flume, which would separate spatial wave evolution from the single-point temporal readout and test the inferred twelve-soliton train directly.
  • If the same device were operated at larger film thickness, the dispersion analysis implies the platform could be tuned from normal to anomalous dispersion, giving access to gravity-capillary solitons and capillary wave turbulence on the same chip.
  • The quantitative claims would be put on firmer ground by an independent calibration of the optomechanical coupling using the second optical mode at 1524 nm; the qualitative observations do not depend on that calibration, but the Ursell-number comparison does.
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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

4 major / 5 minor

Summary. The manuscript demonstrates what the authors call a chip-scale, quantum-enabled wave flume: a 98.5-µm-long silicon optomechanical resonator coated with a 6.7-nm-thick superfluid 4He film, in which third-sound waves are driven by the optomechanically induced superfluid fountain pressure and read out through the cavity's optomechanical frequency shift. From calibrated ringdown traces the authors report (i) backward-leaning waves whose asymmetry parameter evolves to -0.6, attributed to the inverted (van der Waals) nonlinearity of third sound; (ii) near-vertical dispersive shock fronts forming within about one oscillation period; and (iii) fission into a train of up to twelve depression-propagating 'hot' solitons, attributed to an engineered acoustic Bragg-grating dispersion about 35 times the bare hydrodynamic dispersion. The measurements are compared with a custom boundary-integral Euler simulation and a unidirectional KdV model, with qualitative agreement. The device is placed at Ursell numbers near 4×10^8, several orders of magnitude beyond conventional flumes. The paper claims the first direct, time-resolved observation of these long-predicted superfluid nonlinear phenomena.

Significance. If the interpretation holds, this is the first direct time-resolved observation of nonlinear third-sound dynamics (backward steepening, dispersive shock fronts, hot-soliton fission) predicted over fifty years ago, and it establishes a versatile chip platform whose advantages — lithographic geometry control, engineerable dispersion, millisecond measurement cycles, and extreme Ursell numbers — are credible. The paper has real strengths: a drive-asymmetry control (Fig. S4) showing the waveform tilt does not track the drive shape; conservation-checked simulations (mean height conserved to 10^-8, energy to 0.02%); a broad dispersion analysis including an FEM phononic band structure; and explicit acknowledgment of several limitations (single-sided readout inversion, numerical instability at H/h > 0.2, simulation parameter choices). The dip-versus-peak nature of the solitons is preserved under any monotonic height inversion, which robustly supports the 'hot soliton' claim; the same is not true for the quantitative amplitudes, asymmetry values, and the number of resolved dips, all of which inherit any error in the nonlinear calibration.

major comments (4)
  1. [Supplementary §2.3, Eqs. (2)–(3); Table S1] The photodetector-to-film-height inversion in Supplementary §2.3, Eqs. (2)–(3), is the load-bearing link between every quantitative claim in the paper (H ≈ 3 nm, Ur ≈ 4×10^8, asymmetry -0.6, the twelve-soliton count, the cnoidal fit parameters) and the assertion that these features are hydrodynamic in origin, yet its four parameters — G/2π = 5.6 GHz/nm from FEM, κi/2π = 80 GHz and κex/2π = 27 GHz from measurement, the contrast a, and the operating detuning Δ0 (Table S1) — are quoted without uncertainties, and no independent metrology is offered. The readout is significantly nonlinear at the operating point: the wave-induced detuning excursion G·H ≈ 17 GHz is a substantial fraction of the half-width κ/2 ≈ 54 GHz, so the curvature of the Lorentzian flank cannot be neglected. An error in any of the four parameters changes that curvature and, upon inversion, converts a purely linear oscillation into a trace containing higher harmonics and asymmetric distortion — sharp drops, skewness, and multiple apparent dips — which are exactly the observables used as evidence of steepening, shocks, and solitons. The drive-waveform control in Supplementary Fig. S4 varies the actuation waveform, not the readout, and therefore cannot exclude transduction nonlinearity; the text's claim that Fig. S4 'confirm[s] its hydrodynamic origin' is too strong. I request: (i) full error propagation from κ, a, G, and Δ0 to the quoted heights, Ursell number, asymmetry, and soliton count; (ii) a readout cross-check in which the same wave dynamics are recorded on both the blue and the red flank, and ideally with the second optical mode at 1524 nm, whose different G and κ provide an independent transduction channel, verifying that the calibrated η(t) is invariant; and (iii) a synthetic test showing that plausible parameter errors cannot reproduce the observed time evolution of the asymmetry (≈0 at initialization to -0.6 roughly twenty periods later) as the ringdown amplitude decays.
  2. [Main text Figs. 3–4; Supplementary §5 and Fig. S8] The simulation–experiment comparison in Figs. 3 and 4 and Supplementary §5 does not currently constitute a quantitative validation, because several effective parameters are free: the simulated initial amplitude is H = 0.1h (chosen since the code is unstable for H/h > 0.2, whereas the experiment claims H/h ≈ 0.45), the aspect ratio is reduced by ~35× to h/L = 300:1 to encode the dispersion enhancement, and the matching time is selected by evolving a sinusoid for 27 periods 'before matching the profile of multisoliton fission observed in the experiments' (Supplementary §5). In addition, the Euler model is inviscid, while the experimental waves have Q ≈ 50–200 (Supplementary §4.0.2 and §4.2). The visual agreement in Fig. 4B–D is therefore not by itself evidence against alternative explanations. Two specific weaknesses: (a) the 'twelve solitons' are counted in Fig. 4A/B after subtracting an assumed fundamental sinusoid (amplitude 1.5 nm), yet no counting criterion, fit window, or sensitivity analysis for that subtraction is provided; and (b) the caption of Supplementary Fig. S8 states that solitons 'are generated during the drive phase,' so the fission process itself is not temporally resolved, and the claim of fission rests on the post-drive state plus the model. I request a quantitative comparison (e.g., a dip-counting threshold, the inferred count as a function of the subtracted sinusoid's amplitude and phase, and the timing of the first few soliton events in data versus simulation), and a consistency check that the 27-period evolution time for H = 0.1h matches the experimentally observed steepening timescale at H/h ≈ 0.45.
  3. [Supplementary §6.2–6.3, Figs. S15–S16; main text soliton-fission paragraph] The factor-of-35 dispersion enhancement that converts the predicted 'several hundred' solitons into the observed twelve (main text, soliton-fission paragraph; Supplementary §6) is itself partly inferred from that same comparison, which risks circularity. The enhancement combines an FEM band structure of an infinite periodic phononic crystal (Supplementary Fig. S16c) with a weighting factor equal to the 10% spatial extent of the phononic crystal divided by the flume length — an assumption stated in §6.2 but not independently validated — and the resulting dispersion then determines the number of solitons in the comparison simulations that reproduce the observed train. I request that the effective dispersion be validated independently of the soliton count, for example by measuring the eigenmode spectrum of the flume beyond the fundamental (the second free-free mode at ~2Ω and higher modes) and comparing the mode spacings with the dispersion-modified prediction, or by predicting the soliton count of a second device with a different phononic-crystal extent before measuring it.
  4. [Main text 'Third sound waves lean backwards'; Supplementary §3.0.1, Eq. (4), Fig. S6] Two issues affect the characterization of the wave steepening itself. First, the 'wave asymmetry parameter' quoted in the main text (evolving from ≈0 to -0.6 by t = 1.8 ms) is never defined in the main text or the Supplementary Materials; the cited reference (Onorato et al., ref. 32) does not fix a unique sign or normalization convention, and without the defining formula the value -0.6 cannot be checked or reproduced. Second, the late-time cnoidal fit in Supplementary §3.0.1 and Fig. S6 reports m = 0.95 with 'sharper peaks and flatter troughs,' which is the signature of a positive-α (gravity-type) cnoidal wave; for the negative-α van der Waals nonlinearity that the paper uses to explain backward steepening, the corresponding cnoidal solution is the mirror of Eq. (4), with sharp troughs and flat crests. Please provide the asymmetry definition and reconcile this apparent sign reversal of the late-time nonlinear profile with the negative-α interpretation.
minor comments (5)
  1. [Eq. (1); Supplementary Eq. (15)] The symbol α is used both for the KdV nonlinearity coefficient in Eq. (1) and for the van der Waals coefficient in Supplementary Eq. (15); please use distinct symbols to avoid confusion in a manuscript where the sign of α is a central quantity.
  2. [Fig. S15(c,d)] The legend entries for the blue, orange, and dashed-red curves appear to be missing in Fig. S15(c) and (d), making the ratios in panel (d) impossible to attribute to specific mechanisms; please repair the figure legends.
  3. [Supplementary §5, Fig. S14] The text of §5 states hard-wall boundaries at x = ±L/2, while Fig. S14 and the numerical description use the domain x ∈ [0, 2π] with walls at x = 0 and x = π; please make the coordinate convention consistent.
  4. [Discussion] The Discussion's claim of 'sub-picometer sensitivity' is not supported by a measurement or a reference in the manuscript; either provide the supporting calibration or soften the claim.
  5. [Introduction; Supplementary §1.1] Please correct the typos 'superfluids propensity to flow' (Introduction) and the garbled 'Eötvös' rendering (Supplementary §1.1).

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the wave dynamics are compared with independent forward simulations and external predictions; the calibration and dispersion parameters are not constructed from the target observables.

full rationale

The paper's central derivation chain is not circular. Measured photodetector voltages are converted to film height using an independently characterized Lorentzian response and a finite-element optomechanical coupling G/2π = 5.6 GHz/nm; this calibration is not derived from the wave nonlinearities that are claimed as observations. The observed backward leaning, shock fronts, and soliton fission are then compared with two forward models: a KdV equation whose nonlinear and dispersive terms come from standard shallow-water theory, and a custom Euler solver implementing the van der Waals restoring force from superfluid third-sound physics. The inputs to these simulations (sinusoidal initial condition, aspect ratio) are not fit to the measured traces in a way that makes the output equal to the input; the paper explicitly states that the simulated amplitude is smaller than the experimental one because of numerical stability, and the 35-fold dispersion factor is computed from a phononic-crystal band-structure analysis rather than adjusted to reproduce the observed soliton number. Self-citations to prior optomechanical superfluid work appear in the technical methods, but those prior results are published and used as platform parameters, not as a self-referential proof of the present nonlinear observations. The main caveats—unquantified uncertainty in G and the Lorentzian inversion—are accuracy/robustness concerns, not circularity. The claim that the observations are consistent with long-standing external theoretical predictions is therefore supported by an independent comparison, and no step reduces by construction to its own inputs.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central experimental facts (resonance frequency, asymmetry, shock, soliton train) rely on a chain of modeling assumptions: potential-flow hydrodynamics, van der Waals parameters, optical transduction, and the effective dispersion enhancement. The main adjusted parameters are the simulation's initial amplitude and aspect ratio, which are chosen for numerical stability and to emulate a computed but not independently measured dispersion. No new physical entities are introduced.

free parameters (4)
  • Simulation initial wave amplitude (H/h) = 0.1
    The Euler solver is initialized at 10% of the film depth because it becomes numerically unstable above H/h > 0.2; experimental waves reach about 45% of the depth, so the comparison is made at a different amplitude over a longer evolution (Supplementary Section 5).
  • Simulation aspect ratio (L/h) = 300:1
    The custom solver uses L/h = 300 instead of the experimental about 10^4 to emulate the computed 35x dispersion enhancement; this value is derived from the phononic crystal dispersion model but is not directly measured (main text and Supplementary Section 6.3).
  • Effective dispersion enhancement factor = 35
    The ratio of total (capillary plus weighted phononic crystal) dispersion to hydrodynamic dispersion; computed from FEM band structure with a 10% spatial weighting of the phononic crystal, not verified by a separate dispersion measurement (Supplementary Section 6.3).
  • Simulation matching time = 27 wave periods
    The sinusoidal simulation is evolved for 27 periods before its profile is compared to the experimental multisoliton fission trace; the experimental drive lasts about 78 periods, so the matching time is chosen post hoc (Supplementary Section 5).
assumptions (6)
  • domain assumption Superfluid helium at mK temperatures is inviscid, incompressible, and irrotational, so its flow is potential flow
    Used in the hydrodynamic model and boundary integral solver (Supplementary Sections 4 and 5).
  • domain assumption All wave damping in the simulations is neglected; observed decay is attributed to wavelength-dependent evaporation and frequency-dependent damping
    The Euler and KdV solvers are lossless; agreement is only expected for the first few periods (Supplementary Sections 4.1, 4.2).
  • domain assumption The van der Waals coefficient for silicon alpha_vdW = 3.5e-24 m^5 s^-2 is known and constant
    Taken from literature (Refs 30 and 75) and used in third sound speed, dispersion, and simulations (Table S1).
  • ad hoc to paper The acoustic Bragg grating dispersion is captured by an infinite periodic FEM band structure weighted by the 10% spatial extent of the phononic crystal
    This weighting is an assumption; the true device has a finite grating and the wave interacts with it only twice per roundtrip (Supplementary Section 6.2).
  • domain assumption The optical readout is a single-mode Lorentzian and the laser remains on one side of resonance throughout the measurement
    Required for the bijective inversion of Eq. (3); if the laser crosses resonance, the height trace is ambiguous (Supplementary Section 2.3).
  • domain assumption Free-free boundary conditions at both ends of the flume
    Verified indirectly by the mode spectrum showing the second mode at about twice the fundamental frequency and by FEM eigenfrequency agreement (Supplementary Section 4.0.1).

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Pith. "Pith review of Nonlinear wave dynamics on a chip." pith.science (2026). https://pith.science/paper/SITHO7N4

@misc{pith2026250413001,
  author       = {Pith},
  title        = {Pith review of: Nonlinear wave dynamics on a chip},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SITHO7N4}},
  note         = {Machine review of arXiv:2504.13001}
}
read the original abstract

Shallow water waves are a striking example of nonlinear hydrodynamics, giving rise to phenomena such as tsunamis and undular waves. These dynamics are typically studied in hundreds-of-meter-long wave flumes. Here, we demonstrate a chip-scale, quantum-enabled wave flume. The wave flume exploits nanometer-thick superfluid helium films and optomechanical interactions to achieve nonlinearities surpassing those of extreme terrestrial flows. Measurements reveal wave steepening, shock fronts, and soliton fission -- nonlinear behaviors long predicted in superfluid helium but never previously directly observed. Our approach enables lithography-defined wave flume geometries, optomechanical control of hydrodynamic properties, and orders of magnitude faster measurements than terrestrial flumes. Together, this opens a new frontier in hydrodynamics, combining quantum fluids and nanophotonics to explore complex wave dynamics at microscale.

Figures

Figures reproduced from arXiv: 2504.13001 by the authors.

Figure 1
Figure 1. Superfluid wave flume. (A) Landscape of terrestrial shallow wave phenomena and flumes. Conventional wave tanks and flumes cluster in a small region of size and addressable Ursell number, far from extreme terrestrial flows (12). Superfluid-based approaches open up a significantly broader parameter space (see Supplementary Materials, Section 1.1). (B) False color scanning electron microscope image, showing the silicon… view at source ↗
Figure 2
Figure 2. Backwards-leaning waves. (A) i: In conventional hydrodynamics wave crests move faster than troughs (red arrows), leading to forward-leaning waves. ii: forward-leaning waves as observed by a stationary gauge. iii&iv: reverse behavior is predicted for superfluid third sound waves due to their different effective gravity. (B) Laser drive used to initialize and readout large￾amplitude third sound waves. Mean laser power… view at source ↗
Figure 3
Figure 3. Superfluid dispersive shock fronts. (A) Observation of dispersive shock fronts. Red arrows: signatures of soliton fission. (B) Custom Euler model, including counter-propagation and van der Waals nonlinearities, obtained by evolving a sinusoidal wave initialized with am￾plitude H = 0.1h (with computation taking ∼ 4 days on a desktop PC). More details: Supple￾mentary Materials, Section 5. (C) KdV solution obtained usi… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Multi-soliton fission. (A) Observation of multisoliton fission, superimposed over a sinusoidal modulation at the drive frequency with amplitude H = 1.5 nm (dashed red line). (B) Corrected experimental data, with sinusoidal background subtracted. (C) Custom Euler model.…

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Reference graph

Works this paper leans on

78 extracted references · 78 canonical work pages · cited by 1 Pith paper

  1. [1]

    Dutton, M

    Z. Dutton, M. Budde, C. Slowe, L. Hau, Science 293, 663 (2001). 15

    work page 2001

  2. [2]

    Huber, A

    D. Huber, A. Oskooei, X. Casadevall i Solvas, A. Demello, G. Kaigala, Chemical Reviews 118, 2042 (2018)

    work page 2018

  3. [3]

    Garven, Annual Review of Earth and Planetary Sciences 23, 89 (1995)

    G. Garven, Annual Review of Earth and Planetary Sciences 23, 89 (1995)

    work page 1995

  4. [4]

    Burkert, Comptes Rendus

    A. Burkert, Comptes Rendus. Physique 7, 433 (2006)

    work page 2006

  5. [5]

    Amo, et al., Science 332, 1167 (2011)

    A. Amo, et al., Science 332, 1167 (2011)

    work page 2011

  6. [6]

    Aharon-Steinberg, et al., Nature 607, 74 (2022)

    A. Aharon-Steinberg, et al., Nature 607, 74 (2022)

    work page 2022

  7. [7]

    Y . P. Sachkou,et al., Science 366, 1480 (2019)

    work page 2019

  8. [8]

    Stroock, et al., Science 295, 647 (2002)

    A. Stroock, et al., Science 295, 647 (2002)

    work page 2002

Show all 78 references
  1. [9]

    Hereman, Solitons (Springer, 2022), pp

    W. Hereman, Solitons (Springer, 2022), pp. 203–220

    2022

  2. [10]

    Zhang, B

    H. Zhang, B. Geng, Procedia Engineering 116, 905 (2015)

    2015

  3. [11]

    Trillo, et al., Physical Review Letters 117, 144102 (2016)

    S. Trillo, et al., Physical Review Letters 117, 144102 (2016)

    2016

  4. [12]

    Schimmels, V

    S. Schimmels, V . Sriram, I. Didenkulova,Coastal Engineering 110, 32 (2016)

    2016

  5. [13]

    Ursell, Mathematical Proceedings of the Cambridge Philosophical Society 49, 685 (1953)

    F. Ursell, Mathematical Proceedings of the Cambridge Philosophical Society 49, 685 (1953)

    1953

  6. [14]

    J. H. Scholtz, E. O. McLean, I. Rudnick, Physical Review Letters 32, 147 (1974)

    1974

  7. [15]

    Atkins, I

    K. Atkins, I. Rudnick, Progress in Low Temperature Physics (Elsevier, 1970), vol. 6, pp. 37–76

    1970

  8. [16]

    Ichiyanagi, Physics Letters A 55, 283 (1975)

    M. Ichiyanagi, Physics Letters A 55, 283 (1975)

    1975

  9. [17]

    Huberman, Physical Review Letters 41, 1389 (1978)

    B. Huberman, Physical Review Letters 41, 1389 (1978). 16

    1978

  10. [18]

    F. M. Ellis, H. Luo, Journal of Low Temperature Physics89, 115 (1992)

    1992

  11. [19]

    Garrett, Nature 238, 441 (1972)

    C. Garrett, Nature 238, 441 (1972)

    1972

  12. [20]

    Nakajima, S

    S. Nakajima, S. Kurihara, K. Tohdoh, Journal of Low Temperature Physics39, 465 (1980)

    1980

  13. [21]

    Nakajima, K

    S. Nakajima, K. Tohdoh, S. Kurihara, Journal of Low Temperature Physics41, 521 (1980)

    1980

  14. [22]

    Bowen, G

    W. Bowen, G. Milburn, Quantum Optomechanics (CRC Press, 2015)

    2015

  15. [23]

    Aspelmeyer, T

    M. Aspelmeyer, T. J. Kippenberg, F. Marquardt, Reviews of Modern Physics 86, 1391 (2014)

    2014

  16. [24]

    A. J. Archer, et al., Physical Review Fluids 5, 062801 (2020)

    2020

  17. [25]

    Wasserman, et al., Optics Express 30, 30822 (2022)

    W. Wasserman, et al., Optics Express 30, 30822 (2022)

    2022

  18. [26]

    Harris, et al., Nature Physics 12, 788 (2016)

    G. Harris, et al., Nature Physics 12, 788 (2016)

    2016

  19. [27]

    He, et al., Nature Physics 16, 417 (2020)

    X. He, et al., Nature Physics 16, 417 (2020)

    2020

  20. [28]

    Sawadsky, et al., Science Advances 9, eade3591 (2023)

    A. Sawadsky, et al., Science Advances 9, eade3591 (2023)

    2023

  21. [29]

    Korsch, N

    A. Korsch, N. Fiaschi, S. Gr ¨oblacher, Physical Review Applied 22, L041005 (2024)

    2024

  22. [30]

    Baker, et al., New Journal of Physics 18, 123025 (2016)

    C. Baker, et al., New Journal of Physics 18, 123025 (2016)

    2016

  23. [31]

    A. H. Nayfeh, D. T. Mook, Nonlinear Oscillations (Wiley, Weinheim, 2004)

    2004

  24. [32]

    Onorato, S

    M. Onorato, S. Resitori, F. Baronio, eds., Rogue and Shock Waves in Nonlinear Dispersive Media, vol. 926 of Lecture Notes in Physics (Springer International Publishing, Cham, 2016)

    2016

  25. [33]

    Zabusky, M

    N. Zabusky, M. Kruskal, Physical Review Letters 15, 240 (1965). 17

    1965

  26. [34]

    Redor, E

    I. Redor, E. Barth ´elemy, H. Michallet, M. Onorato, N. Mordant, Physical Review Letters 122, 214502 (2019)

    2019

  27. [35]

    D. J. Bergman, Physical Review A 3, 2058 (1971)

    1971

  28. [36]

    Generazio, R

    E. Generazio, R. Reed, Journal of Low Temperature Physics57, 501 (1984)

    1984

  29. [37]

    Sfendla,et al., npj Quantum Information 7, 1 (2021)

    Y . Sfendla,et al., npj Quantum Information 7, 1 (2021)

    2021

  30. [38]

    Skolianos, A

    G. Skolianos, A. Arora, M. Bernier, M. Digonnet, Journal of Physics D: Applied Physics 49, 463001 (2016)

    2016

  31. [39]

    Kono, S.-i

    K. Kono, S.-i. Kobayashi, W. Sasaki, Journal of the Physical Society of Japan 50, 721 (1981)

    1981

  32. [40]

    M. J. McKenna, R. J. Stanley, E. DiMasi, J. D. Maynard, Physica B: Condensed Matter 165-166, 603 (1990)

    1990

  33. [41]

    Kaminski, L

    S. Kaminski, L. L. Martin, S. Maayani, T. Carmon, Nature Photonics 10, 758 (2016)

    2016

  34. [42]

    A. D. Kashkanova, et al., Nature Physics 13, 74 (2017)

    2017

  35. [43]

    Zhang, et al., Nature 600, 75 (2021)

    J. Zhang, et al., Nature 600, 75 (2021)

    2021

  36. [44]

    Falcon, C

    E. Falcon, C. Laroche, S. Fauve, Physical Review Letters 98, 094503 (2007)

    2007

  37. [45]

    Kochkov, et al., Proceedings of the National Academy of Sciences 118, e2101784118 (2021)

    D. Kochkov, et al., Proceedings of the National Academy of Sciences 118, e2101784118 (2021)

    2021

  38. [46]

    Zhu, et al., Industrial & Engineering Chemistry Research 61, 9901 (2022)

    L.-T. Zhu, et al., Industrial & Engineering Chemistry Research 61, 9901 (2022)

    2022

  39. [47]

    Mojgani, A

    R. Mojgani, A. Chattopadhyay, P. Hassanzadeh, Journal of Advances in Modeling Earth Systems 16, e2023MS004033 (2024). 18

    2024

  40. [48]

    G. A. El, A. M. Kamchatnov, Physical Review Letters 95, 204101 (2005)

    2005

  41. [49]

    G. A. El, Journal of Statistical Mechanics: Theory and Experiment 2021, 114001 (2021)

    2021

  42. [50]

    T. B. Benjamin, J. E. Feir, Journal of Fluid Mechanics 27, 417 (1967)

    1967

  43. [51]

    Deike, M

    L. Deike, M. Berhanu, E. Falcon, Physical Review E 89, 023003 (2014)

    2014

  44. [52]

    L. V . Abdurakhimov,et al., Physical Review E 91, 023021 (2015)

    2015

  45. [53]

    Y . S. Kivshar, B. A. Malomed,Reviews of Modern Physics 61, 763 (1989)

    1989

  46. [54]

    Hedges, Proceedings of the Institution of Civil Engineers-Water Maritime and Energy 112, 111 (1995)

    T. Hedges, Proceedings of the Institution of Civil Engineers-Water Maritime and Energy 112, 111 (1995)

    1995

  47. [55]

    M ´ehaut´e, An Introduction to Hydrodynamics and Water Waves(Springer Berlin Heidel- berg, 1976)

    B. M ´ehaut´e, An Introduction to Hydrodynamics and Water Waves(Springer Berlin Heidel- berg, 1976)

    1976

  48. [56]

    C. T. Bishop, M. A. Donelan, Coastal Engineering 11, 309 (1987)

    1987

  49. [57]

    F. M. Ellis, L. Li, Physical review letters 71, 1577 (1993)

    1993

  50. [58]

    F. M. Ellis, H. Luo, Physical Review B 39, 2703 (1989)

    1989

  51. [59]

    P. A. Madsen, D. R. Fuhrman, H. A. Sch ¨affer, Journal of Geophysical Research: Oceans 113, 2008JC004932 (2008)

    2008

  52. [60]

    F. M. Ellis, R. B. Hallock, Review of Scientific Instruments 54, 751 (1983)

    1983

  53. [61]

    Donnelly, C

    R. Donnelly, C. Barenghi, Journal of Physical and Chemical Reference Data 27, 1217 (1998)

    1998

  54. [62]

    G. I. Harris, et al., Optics Express 28, 22450 (2020). 19

    2020

  55. [63]

    Gr ¨oblacher, J

    S. Gr ¨oblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, O. Painter, Applied Physics Letters 103, 181104 (2013)

    2013

  56. [64]

    Baker, On-chip nano-optomechanical whispering gallery resonators, Ph.D

    C. Baker, On-chip nano-optomechanical whispering gallery resonators, Ph.D. thesis, Paris 7 (2013)

    2013

  57. [65]

    Simmons, et al., Physical Review Letters 125, 180401 (2020)

    S. Simmons, et al., Physical Review Letters 125, 180401 (2020)

    2020

  58. [66]

    M. E. Mossman, M. A. Hoefer, K. Julien, P. G. Kevrekidis, P. Engels, Nature Communica- tions 9, 4665 (2018)

    2018

  59. [67]

    Souris, X

    F. Souris, X. Rojas, P. Kim, J. Davis, Physical Review Applied 7, 044008 (2017)

    2017

  60. [68]

    K. R. Atkins, Canadian Journal of Physics 32, 347 (1954)

    1954

  61. [69]

    McAuslan, et al., Physical Review X 6, 021012 (2016)

    D. McAuslan, et al., Physical Review X 6, 021012 (2016)

    2016

  62. [70]

    Roberts, IMA Journal of Applied Mathematics 31, 13 (1983)

    A. Roberts, IMA Journal of Applied Mathematics 31, 13 (1983)

    1983

  63. [71]

    Smith, A

    D. Smith, A. Roberts, Physics of Fluids 11, 1051 (1999)

    1999

  64. [72]

    Forstner, et al., New Journal of Physics 21, 053029 (2019)

    S. Forstner, et al., New Journal of Physics 21, 053029 (2019)

    2019

  65. [73]

    Ouellette, Optics Letters 12, 847 (1987)

    F. Ouellette, Optics Letters 12, 847 (1987)

    1987

  66. [74]

    Kurosu, D

    M. Kurosu, D. Hatanaka, K. Onomitsu, H. Yamaguchi, Nature Communications 9, 1331 (2018)

    2018

  67. [75]

    E. S. Sabisky, C. H. Anderson, Physical Review Letters 30, 1122 (1973)

    1973

  68. [76]

    A. Gray, E. Abbena, S. Salamon, Modern differential geometry of curves and surfaces with Mathematica® (Chapman and Hall/CRC, 2017)

    2017

  69. [77]

    Perrard, L

    S. Perrard, L. Deike, C. Duch ˆene, C.-T. Pham, Physical Review E 92, 011002 (2015). 20 Supplementary Materials for Nonlinear wave dynamics on a chip Matthew T. Reeves,1∗ Walter W. Wasserman,1∗ Raymond A. Harrison,1 Igor Marinkovi´c,1 Nicole Luu,1 Andreas Sawadsky,1 Yasmine L....

    2015

  70. [78]

    +uQyNRflh6ZfpBt0Osl+e4sjuBk=

    Fitting parameters: trough elevation η2 = 6.29 nm; wave height H = 1.18 nm; elliptic parameterm = 0.949. main text. The wave initially steepens in the first period of free evolution after the drive is switched off (t∼ 1.8 to 1.9 ms). This leads to the formation of a near verti...

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Reviewed August 16, 2026 · model on record in the stance chip above.