{
  "annotation_id": "7011a3cd-351b-43d2-8107-fdfc8be085e3",
  "date_created": "2026-02-17T05:53:11.949000Z",
  "date_modified": "2026-02-17T05:53:11.949000Z",
  "file_hash": "0d54b0b2e0e6ef4f1f8f70dd080ca51c098f6210153bd7ebee764069fc65aae9",
  "private": false,
  "record": {
    "abstract": "This work investigates the initial value problem (IVP) for the two-parameter family of dispersive wave equations known as the Majda-McLaughlin-Tabak (MMT) model, which arises in the weak turbulence theory of random waves. The MMT model can be viewed as a derivative nonlinear Schr\\\"odinger (dNLS) equation where both the nonlinearity and dispersion involve nonlocal fractional derivatives. The purpose of this study is twofold: first, to establish a sharp well-posedness theory for the MMT model; and second, to identify the critical threshold for the derivative in the nonlinearity relative to the dispersive order required to ensure well-posedness. As a by-product, we establish sharp well-posedness for non-local fractional dNLS equations; notably, our results resolve the regularity endpoint left open in https://www.aimsciences.org/article/doi/10.3934/dcdsb.2022039 .",
    "arxiv_id": "2601.07771",
    "authors": [
      "Mahendra Panthee",
      "James Patterson",
      "Yuzhao Wang"
    ],
    "categories": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On the well-posedness of the initial value problem for the MMT model",
    "url": "https://arxiv.org/abs/2601.07771",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "685d958f-f312-4b2c-a7f8-6c719bcd1299",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}