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pith:LDMMWDGZ

pith:2025:LDMMWDGZMXQ75Y655NPLWTBP4W

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Perturbative nonlinear J-matrix method of scattering in two dimensions

A. D. Alhaidari, T. J. Taiwo, U. Al Khawaja

A perturbative nonlinear J-matrix method yields the scattering matrix for the two-dimensional nonlinear Schrödinger equation with circular symmetry and detects energy-dependent bifurcations.

arxiv:2511.14519 v1 · 2025-11-18 · quant-ph · nlin.SI

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Claims

C1strongest claim

We obtain the scattering matrix for the time-independent nonlinear Schrödinger equation in two dimensions with circular symmetry... At certain value(s) of the energy, we observe the occurrence of bifurcation with two stable solutions.

C2weakest assumption

The linearization of products of orthogonal polynomials remains accurate enough under the perturbative treatment to capture the essential nonlinear effects without introducing uncontrolled errors in the scattering matrix or the bifurcation points.

C3one line summary

A perturbative extension of the J-matrix method yields scattering matrices for the 2D nonlinear Schrödinger equation with ψ³ and ψ⁵ nonlinearities, exhibiting bifurcations at specific energies.

References

28 extracted · 28 resolved · 0 Pith anchors

[1] G. P. Agrawal, Nonlinear Fiber Optics, 6th ed. (San Diego: Academic Press, 2019) 2019

[2] S. B. Pope, Turbulent Flows (Cambridge: Cambridge University Press, 2000) 2000

[3] M. Kono and M. M. Skoric, Nonlinear Physics of Plasmas (Berlin: Springer, 2010) 2010

[4] R. C. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, 2nd ed. (Oxford: Oxford University Press, 2000) 2000

[5] P. G. Kevrekidis, D . J. Frantzeskakis, and R . Carretero-González (Eds.) Emergent Nonlinear Phenomena in Bose -Einstein Condensates: Theory and Experiment (Berlin: Springer, 2008) 2008

Formal links

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Receipt and verification

First computed	2026-05-20T01:05:02.209845Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58d8cb0cd965e1fee3ddeb5ebb4c2fe586f2cca33d75fb62b07e2955205f0e6c

Aliases

arxiv: 2511.14519 · arxiv_version: 2511.14519v1 · doi: 10.48550/arxiv.2511.14519 · pith_short_12: LDMMWDGZMXQ7 · pith_short_16: LDMMWDGZMXQ75Y65 · pith_short_8: LDMMWDGZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LDMMWDGZMXQ75Y655NPLWTBP4W \
  | 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: 58d8cb0cd965e1fee3ddeb5ebb4c2fe586f2cca33d75fb62b07e2955205f0e6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5dd8d3e806c4d23d26c74b586b308b0131a4aad38a35f03affa0130e0b1346d1",
    "cross_cats_sorted": [
      "nlin.SI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-11-18T14:15:26Z",
    "title_canon_sha256": "11e43013253b0290f2ac9642c50bd149c647e583cae89026215e6c970cbc873b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.14519",
    "kind": "arxiv",
    "version": 1
  }
}