Pith Number

pith:DPSBGZ6R

pith:2026:DPSBGZ6RV25J4YLZSW2T6UMT6N

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New soliton solutions for Chen-Lee-Liu and Burgers hierarchies and its B\"acklund transformations

C. P. Constantinidis, G. V. Lobo, H. Aratyn, J. F. Gomes, T. C. Santiago, Y. F. Adans

Vertex operators in a Heisenberg algebra produce closed-form multi-soliton solutions for the Burgers hierarchy.

arxiv:2603.23665 v2 · 2026-03-24 · nlin.SI · hep-th · math-ph · math.MP

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Claims

C1strongest claim

A judicious choice of vertices yields in a closed form a particular set of multi soliton solutions for the Burgers hierarchy. We develop and analyze a class of gauge-Bäcklund transformations that generate further multi soliton solutions from those obtained by dressing method.

C2weakest assumption

The framework of Riemann-Hilbert-Birkhoff decomposition with the constant grade two generator allows both zero and constant non-zero vacua to be realized within a centerless Heisenberg algebra, enabling the dressing method to produce the claimed soliton solutions.

C3one line summary

New soliton solutions for Chen-Lee-Liu and Burgers hierarchies are derived via dressing methods on zero and non-zero vacua, classified by vertex operators, and extended by gauge-Bäcklund transformations.

References

39 extracted · 39 resolved · 6 Pith anchors

[1] V. G. Drinfel’d, V. V. Sokolov, Lie algebras and equations of Korteweg-de Vries type, Journal of Soviet Mathematics 30 (2) (1985) 1975–2036.doi:10.1007/BF02105860. URL http://link.springer.com/10.1007 1985 · doi:10.1007/bf02105860

[2] M. F. De Groot, T. J. Hollowood, J. L. Miramontes, Generalized Drinfel’d-Sokolov hierarchies, Communications in Mathematical Physics 145 (1) (1992) 57–84.doi:10.1007/BF02099281. URL http://link.spring 1992 · doi:10.1007/bf02099281

[3] H. Aratyn, L. A. Ferreira, J. F. Gomes, A. H. Zimerman, The complex sine-Gordon equation as a symmetry flow of the AKNS hierarchy, Journal of Physics A: Mathematical and General 33 (35) (2000) L331–L3 2000 · doi:10.1088/0305-4470/33/35/101

[4] Negative Even Grade mKdV Hierarchy and its Soliton Solutions 2009 · doi:10.1088/1751-8113/42/44/4452

[5] URL http://arxiv.org/abs/2304.01749 2023 · doi:10.1007/jhep08(2023)160

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Receipt and verification

First computed	2026-05-17T23:38:59.553922Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1be41367d1aeba9e617995b53f5193f36dd4bca1896a4c29766f7550bcf84af7

Aliases

arxiv: 2603.23665 · arxiv_version: 2603.23665v2 · doi: 10.48550/arxiv.2603.23665 · pith_short_12: DPSBGZ6RV25J · pith_short_16: DPSBGZ6RV25J4YLZ · pith_short_8: DPSBGZ6R

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/DPSBGZ6RV25J4YLZSW2T6UMT6N \
  | 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: 1be41367d1aeba9e617995b53f5193f36dd4bca1896a4c29766f7550bcf84af7

Canonical record JSON

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      "math-ph",
      "math.MP"
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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "nlin.SI",
    "submitted_at": "2026-03-24T19:10:15Z",
    "title_canon_sha256": "5b8eeb99f318fc4cda72b68193729bf63d088978272f053f265182758d423721"
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