Pith Number

pith:7XQS7H74

pith:2026:7XQS7H746J6GHCCAFYETW5DAV5

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The unified transform for Burgers' equation: Application to unsaturated flow in finite interval

Athanasios Paraskevopoulos, Konstantinos Kalimeris, Leonidas Mindrinos

The Unified Transform Method supplies an explicit integral representation for solutions of the linearized Burgers equation on a finite interval.

arxiv:2605.11788 v2 · 2026-05-12 · math.AP · math-ph · math.MP

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Claims

C1strongest claim

The Unified Transform Method gives an explicit integral representation of the solution to the linearized Burgers' equation on a finite interval, which when evaluated numerically matches classical Fourier series solutions exactly but with better convergence and stability.

C2weakest assumption

The physical assumptions of constant diffusivity and quadratic relationship between hydraulic conductivity and water content hold, allowing Richards' equation to reduce to Burgers' equation that can be linearized via Hopf-Cole transformation.

C3one line summary

Unified Transform Method applied to linearized Burgers' equation on finite interval yields explicit integral solution with better convergence than Fourier series for unsaturated flow models.

Receipt and verification

First computed	2026-05-26T01:03:33.523268Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fde12f9ffcf27c6388402e093b7460af7cb63cc9ddc36b5a2629833073e66428

Aliases

arxiv: 2605.11788 · arxiv_version: 2605.11788v2 · doi: 10.48550/arxiv.2605.11788 · pith_short_12: 7XQS7H746J6G · pith_short_16: 7XQS7H746J6GHCCA · pith_short_8: 7XQS7H74

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7XQS7H746J6GHCCAFYETW5DAV5 \
  | 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: fde12f9ffcf27c6388402e093b7460af7cb63cc9ddc36b5a2629833073e66428

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a74b51b6efa5e7b843cd915f349c50e6fc605cbb483c7347b37955119bfb0d48",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-12T08:53:54Z",
    "title_canon_sha256": "08cfb452924a9f8a62d18c43cd9113d6e0ae1b6a6f13d3cc1e7ad3fb4c1baa37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11788",
    "kind": "arxiv",
    "version": 2
  }
}