Pith Number

pith:KD5JOT5E

pith:2026:KD5JOT5EEWLXIVKDLKOTPQDVF6

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Stability of localized solutions to lattice dynamical systems

Bocheng Ruan, Jack M. Hughes, Jason J. Bramburger

For well-separated localized patterns in lattices the Evans function factorizes into front and back contributions to count unstable eigenvalues explicitly.

arxiv:2605.12605 v1 · 2026-05-12 · nlin.PS

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Claims

C1strongest claim

We prove that, for well-separated regions of localization, the Evans function asymptotically factorizes into contributions from the underlying fronts and backs, allowing explicit counting of unstable eigenvalues.

C2weakest assumption

The localized regions must be well-separated so that the asymptotic factorization of the Evans function holds; this separation assumption is required for the explicit counting result.

C3one line summary

For well-separated localized solutions on lattices, the discrete Evans function asymptotically factorizes into front and back contributions, enabling explicit counting of unstable eigenvalues.

References

21 extracted · 21 resolved · 0 Pith anchors

[1] N. Balmforth, R. Craster, and P. Kevrekidis. Being stable and discrete. Physica D: Nonlinear Phenomena, 135(3-4):212–232, 2000 2000

[2] E. Bergland, J. J. Bramburger, and B. Sandstede. Localized synchronous patterns in weakly coupled bistable oscillator systems. Physica D: Nonlinear Phenomena , 472:134537, 2025 2025

[3] W.-J. Beyn and J.-M. Kleinkauf. The numerical computation of homoclinic orbits for maps. SIAM journal on numerical analysis , 34(3):1207–1236, 1997 1997

[4] J. J. Bramburger. Isolas of multi-pulse solutions to lattice dynamical systems. Proceedings of the Royal Society of Edinburgh Section A: Mathematics , 151(3):916–952, 2021. 29 2021

[5] J. J. Bramburger, D. J. Hill, and D. J. Lloyd. Localized patterns. arXiv preprint arXiv:2404.14987, 2024 2024

Receipt and verification

First computed	2026-05-18T03:10:00.802523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50fa974fa425977455435a9d37c0752f941faacb128436cee03bd656b8af32a8

Aliases

arxiv: 2605.12605 · arxiv_version: 2605.12605v1 · doi: 10.48550/arxiv.2605.12605 · pith_short_12: KD5JOT5EEWLX · pith_short_16: KD5JOT5EEWLXIVKD · pith_short_8: KD5JOT5E

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KD5JOT5EEWLXIVKDLKOTPQDVF6 \
  | 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: 50fa974fa425977455435a9d37c0752f941faacb128436cee03bd656b8af32a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd5aa8328f4d9d182255d7f8b6ba67c7ada954ffbae8d1139b85a6a9d27b400a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "nlin.PS",
    "submitted_at": "2026-05-12T18:00:09Z",
    "title_canon_sha256": "c5e79096aefe36c9554bc3d92165a0a6fb4bb747d3299ec867b5b0882104a78a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12605",
    "kind": "arxiv",
    "version": 1
  }
}