Pith Number

pith:UUWNHMJP

pith:2026:UUWNHMJPFIKW3WOCHXSBBMP4M6

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Generalized Error Bounds in the Recovery of Solitary Wave Profiles

Daniel Sinambela

Perturbations in wave speed, depth, and bed pressure yield sublinear L² errors when recovering solitary wave profiles via Constantin's formula.

arxiv:2605.15590 v1 · 2026-05-15 · math.CA · math-ph · math.MP · nlin.PS

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Record completeness

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Claims

C1strongest claim

We derive an L² error estimate for the reconstructed profile. The proof uses the hodograph transform, holomorphic extension arguments, and Paley--Wiener Fourier-decay estimates, yielding stability estimates with sublinear dependence on the perturbation size.

C2weakest assumption

The underlying flow is a two-dimensional irrotational solitary water wave satisfying the conditions that allow the hodograph transform and holomorphic extension to be applied, and the perturbations in wave speed, undisturbed depth, and dynamic pressure are sufficiently small for the estimates to hold.

C3one line summary

Derives L2 stability estimates with sublinear dependence on perturbation size for Constantin's solitary wave profile reconstruction under errors in speed, depth, and pressure data.

References

27 extracted · 27 resolved · 0 Pith anchors

[1] Wave Motion , FJOURNAL = 2017 · doi:10.1016/j.wavemoti.2017.08.003

[2] Clamond, Didier , TITLE =. J. Fluid Mech. , FJOURNAL =. 2013 , PAGES =. doi:10.1017/jfm.2013.253 , URL = 2013 · doi:10.1017/jfm.2013.253

[3] Henry, D. and Thomas, G. P. , TITLE =. Philos. Trans. Roy. Soc. A , FJOURNAL =. 2018 , NUMBER =. doi:10.1098/rsta.2017.0102 , URL = 2018 · doi:10.1098/rsta.2017.0102

[4] Clamond, Didier and Henry, David , TITLE =. J. Fluid Mech. , FJOURNAL =. 2020 , PAGES =. doi:10.1017/jfm.2020.729 , URL = 2020 · doi:10.1017/jfm.2020.729

[5] Journal of Fluid Mechanics , volume= 2023

Formal links

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Receipt and verification

First computed	2026-05-20T00:01:06.957725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a52cd3b12f2a156dd9c23de410b1fc67aa0a1a4b0c32cb072948b40e4209810c

Aliases

arxiv: 2605.15590 · arxiv_version: 2605.15590v1 · doi: 10.48550/arxiv.2605.15590 · pith_short_12: UUWNHMJPFIKW · pith_short_16: UUWNHMJPFIKW3WOC · pith_short_8: UUWNHMJP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UUWNHMJPFIKW3WOCHXSBBMP4M6 \
  | 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: a52cd3b12f2a156dd9c23de410b1fc67aa0a1a4b0c32cb072948b40e4209810c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a88779e6193e4c962872c7e3f29e99b2441af050f1f96649f0c88873e5f3f3b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "nlin.PS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-05-15T04:00:12Z",
    "title_canon_sha256": "4e1db536c36a72cde5aa84ee227ccdf33f14208ea6b61753c359bb3231be3f07"
  },
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  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}