Pith Number

pith:JVWUNYB7

pith:2026:JVWUNYB76DSW7XEXQ75FJAVYXZ

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Orbital stability of black solitons for quasilinear Schr\"odinger equations with nonzero conditions at infinity

Erwan Le Quiniou

The black soliton is orbitally stable in the energy space for quasilinear Schrödinger equations when the Vakhitov-Kolokolov slope condition holds.

arxiv:2605.13629 v1 · 2026-05-13 · math.AP

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Record completeness

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4 Citations open

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Claims

C1strongest claim

Our main result is the orbital stability of the black soliton in the energy space, provided that the Vakhitov-Kolokolov (VK) slope condition holds; namely, that the derivative of the momentum with respect to the speed is negative at zero.

C2weakest assumption

The analysis of minimizing sequences for the variational problem (infimum not attained) together with the sufficient conditions on the quasilinear nonlinearities that ensure existence of the local soliton branch parameterized by speed.

C3one line summary

Black solitons are orbitally stable in the energy space when the derivative of momentum with respect to speed is negative at zero speed.

References

60 extracted · 60 resolved · 0 Pith anchors

[1] M. A. Alejo and A. J. Corcho. Orbital stability of the black soliton for the quintic Gross- Pitaevskii equation.Rev. Mat. Iberoam., 40(5):1731–1780, 2024 2024

[2] C. O. Alves, Y. Wang, and Y. Shen. Soliton solutions for a class of quasilinear Schrödinger equations with a parameter.J. Differential Equations, 259(1):318–343, 2015 2015

[3] C. Audiard. Small energy traveling waves for the Euler-Korteweg system.Nonlinearity, 30(9):3362–3399, 2017 2017

[4] C. Audiard and B. Haspot. Global well-posedness of the Euler-Korteweg system for small irrotational data.Comm. Math. Phys., 351(1):201–247, 2017 2017

[5] L. Baldelli, B. Bieganowski, and J. Mederski. Traveling waves for nonlinear Schrödinger equations, 2024. Preprint arXiv:2406.03910. 44 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:17.775090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d6d46e03ff0e56fdc9787fa5482b8be5fee4af73ecae6bd65ef37a67c127db4

Aliases

arxiv: 2605.13629 · arxiv_version: 2605.13629v1 · doi: 10.48550/arxiv.2605.13629 · pith_short_12: JVWUNYB76DSW · pith_short_16: JVWUNYB76DSW7XEX · pith_short_8: JVWUNYB7

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JVWUNYB76DSW7XEXQ75FJAVYXZ \
  | 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: 4d6d46e03ff0e56fdc9787fa5482b8be5fee4af73ecae6bd65ef37a67c127db4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa8503200b2165daf67aaf81eeb3cd44f3fe1a54d5366265f8e6bb1d0e770121",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T14:57:07Z",
    "title_canon_sha256": "5ae0efd6865e78da0479188d34215c5ea03b836bf769251bb470559173703531"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13629",
    "kind": "arxiv",
    "version": 1
  }
}