Pith Number

pith:EPUD6L6F

pith:2026:EPUD6L6F3EJ7NKNTR6RC6QW7LO

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A study of variational single solitary waves governed by the conservative-extended KdV equation with applications to shallow water dispersive shocks

Hamid Said, Saleh Baqer

Variational methods produce simple solitary wave solutions for the conservative extended KdV equation that agree with numerical simulations and apply to shallow water dispersive shocks.

arxiv:2605.14024 v1 · 2026-05-13 · nlin.PS · physics.flu-dyn

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Claims

C1strongest claim

Theoretical predictions show excellent agreement with numerical simulations for the solitary wave solutions applied to shallow water classical undular bores and non-classical resonant dispersive shocks.

C2weakest assumption

The extended KdV equation with the four additional terms accurately captures the dynamics of the full dispersive Euler shallow water equations under the weakly nonlinear and long-wave approximations.

C3one line summary

Variational solitary wave solutions for the conservative extended KdV equation agree with numerics and apply to shallow water dispersive shocks.

References

56 extracted · 56 resolved · 0 Pith anchors

[1] G.B. Whitham, Linear and Nonlinear Waves, J. Wiley and Sons, New York (1974) 1974

[2] Kamchatnov, Nonlinear periodic waves and their modulations: an introdu ctory course, World Scientiﬁc, Singapore (2000) 2000

[3] Shallow water waves–exten ded Korteweg-de Vries equa- tions, 2018

[4] I.M. Gelfand and S.V. Fomin, Calculus of variations , Revised and translated by R. A. Silverman, Dover Publications, New York (2000) 2000

[5] Trefethen, Spectral methods in MATLAB 2000

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:12.912404Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23e83f2fc5d913f6a9b38fa22f42df5b93b271194c7892cda48d03e4940d2f24

Aliases

arxiv: 2605.14024 · arxiv_version: 2605.14024v1 · doi: 10.48550/arxiv.2605.14024 · pith_short_12: EPUD6L6F3EJ7 · pith_short_16: EPUD6L6F3EJ7NKNT · pith_short_8: EPUD6L6F

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EPUD6L6F3EJ7NKNTR6RC6QW7LO \
  | 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: 23e83f2fc5d913f6a9b38fa22f42df5b93b271194c7892cda48d03e4940d2f24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "409bf93a06f0c1d7b206ce0c69214d4caab7aae900e4119bc6a53e4ef7ea1c58",
    "cross_cats_sorted": [
      "physics.flu-dyn"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "nlin.PS",
    "submitted_at": "2026-05-13T18:36:46Z",
    "title_canon_sha256": "0631936283dfda96e75079cf234baf7d251b3bba9097de692941443d884c02f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14024",
    "kind": "arxiv",
    "version": 1
  }
}