Pith Number

pith:AHCMS2ZH

pith:2026:AHCMS2ZHXM5PTPRGT4Y5LAGPQF

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Rigorous Construction of Stop-and-Go Waves in the Optimal Velocity Model via a Difference-Differential Equation

Kota Ikeda, Tomoyuki Miyaji

The optimal velocity model admits rigorous heteroclinic traveling waves and large-period periodic stop-and-go solutions for sufficiently steep velocity functions.

arxiv:2605.15629 v1 · 2026-05-15 · math.DS

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Claims

C1strongest claim

We rigorously prove the existence of heteroclinic traveling waves for sufficiently steep OV functions, the existence of homoclinic solutions with a necessary condition on the amplitude parameter, and the existence of large-period periodic solutions comprising alternating transition layers and quasi-uniform states under the global road-length constraint.

C2weakest assumption

The optimal velocity function must be sufficiently steep and approach a step function so that the singular-limit analysis produces sharp, explicitly constructible transition layers; this premise is invoked in the traveling-wave formulation and the singular-limit construction.

C3one line summary

Rigorous existence proofs for heteroclinic, homoclinic, and periodic traveling waves in the optimal velocity model via singular-limit analysis of a difference-differential equation.

References

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[1] S. M. Allen and J. W. Cahn. A microscopic theory for antiphase bou ndary motion and its application to antiphase domain coarsening. Acta Metallurgica, 27(6):1085–1095, 1979 1979

[2] M. Bando, K. Hasebe, K. Nakanishi, A. Nakayama, A. Shibata, an d Y. Sugiyama. Phenomenological study of dynamical model of traﬃc ﬂow. Journal de Physique I , 5(11):1389–1399, 1995 1995

[3] M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama . Structure stability of congestion in traﬃc dynamics. Japan Journal of Industrial and Applied Mathematics , 11:203–223, 1994 1994

[4] M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama . Dynamical model of traﬃc conges- tion and numerical simulation. Physical Review E , 51(2):1035, 1995 1995

[5] N. Bellomo, M. Delitala, and V. Coscia. On the mathematical theory of vehicular traﬃc ﬂow I: Fluid dynamic and kinetic modelling. Mathematical Models and Methods in Applied Sciences , 12(12):1801– 184 2002

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Receipt and verification

First computed	2026-05-20T00:01:08.970360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01c4c96b27bb3af9be269f31d580cf8174e33e3e0f79a2ee896da560e2570ada

Aliases

arxiv: 2605.15629 · arxiv_version: 2605.15629v1 · doi: 10.48550/arxiv.2605.15629 · pith_short_12: AHCMS2ZHXM5P · pith_short_16: AHCMS2ZHXM5PTPRG · pith_short_8: AHCMS2ZH

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/AHCMS2ZHXM5PTPRGT4Y5LAGPQF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 01c4c96b27bb3af9be269f31d580cf8174e33e3e0f79a2ee896da560e2570ada

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "ab35f05acf1ff09dd465a381bdf77b3999a732a59dca37b7d0453a730a342706",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-15T05:28:42Z",
    "title_canon_sha256": "2c4cfafee2b1958a242c201fef110aae9b0961713bee7daf69faa02142098549"
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