Pith Number

pith:IQCTPAPO

pith:2026:IQCTPAPOZ4LIBWZKTMFV27HP6X

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Soliton-like solutions of the Camassa--Holm equation with variable coefficients and a small dispersion

Valerii Samoilenko, Yuliia Samoilenko

Asymptotic expansions construct soliton- and peakon-like solutions to arbitrary accuracy for the variable-coefficient Camassa-Holm equation with small dispersion.

arxiv:2604.17348 v2 · 2026-04-19 · math-ph · math.MP

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Claims

C1strongest claim

Theorems on the asymptotic accuracy of the constructed asymptotic solutions have been proved; in the one-phase case the solvability of higher-order singular corrections is established in suitable functional spaces, enabling construction of asymptotic solutions to arbitrary accuracy in a small parameter.

C2weakest assumption

The precise definition of the main singular term (the leading peakon or soliton profile) is chosen so that the resulting correction equations remain solvable at every order; this choice is stated to play a central role but is not derived from first principles within the paper.

C3one line summary

The paper constructs asymptotic expansions for one-phase and two-phase soliton-like and peakon-like solutions of the variable-coefficient Camassa-Holm equation with small dispersion and proves their asymptotic accuracy.

References

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[1] R. Camassa and D. Holm. An integrable shallow water equation with peaked soliton.Phys. Rev. Lett., 71(11):1661–1664, 1993. doi: 10.1103/PhysRevLett.71.1661 1993 · doi:10.1103/physrevlett.71.1661

[2] H. Lundmark and J. Szmigielski. A view of the peakon world through the lens of approximation theory.Physica D: Nonlinear Phenomena, 440: 133446, 2022. doi: 10.1016/j.physd.2022.133446. 47 2022 · doi:10.1016/j.physd.2022.133446

[3] H. Lundmark and B. Shuaib. Ghostpeakons and characteristic curves for theCamassa–Holm, Degasperis–ProcesiandNovikovequations.Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 15:

[4] doi: 10.3842/SIGMA.2019.017 2019 · doi:10.3842/sigma.2019.017

[5] B. Fuchssteiner and A. S. Fokas. Symplectic structures, their Bäcklund transformations and hereditary symmetries.Physica D: Nonlinear Phe- nomena, 4(1):47–66, 1981/1982. doi: 10.1016/0167-2789(81)9000 1981 · doi:10.1016/0167-2789(81)90004-x

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Receipt and verification

First computed	2026-05-20T00:01:41.420850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44053781eecf1680db2a9b0b5d7ceff5cf2933d9535a71105cc142720127afbd

Aliases

arxiv: 2604.17348 · arxiv_version: 2604.17348v2 · doi: 10.48550/arxiv.2604.17348 · pith_short_12: IQCTPAPOZ4LI · pith_short_16: IQCTPAPOZ4LIBWZK · pith_short_8: IQCTPAPO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IQCTPAPOZ4LIBWZKTMFV27HP6X \
  | 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: 44053781eecf1680db2a9b0b5d7ceff5cf2933d9535a71105cc142720127afbd

Canonical record JSON

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    "abstract_canon_sha256": "63dab6ed94c02e3aa05319715d0ad41f99f3044623afba30fe42ca8c613b9877",
    "cross_cats_sorted": [
      "math.MP"
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    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-04-19T09:44:07Z",
    "title_canon_sha256": "b00d85074aa073040c9343ffb017890b2294579a135905e1dd3433668279f8bf"
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}