{
  "id": "2207.07248",
  "version": "v1",
  "published": "2022-07-15T01:13:50.000Z",
  "updated": "2022-07-15T01:13:50.000Z",
  "title": "Modified Scattering of Cubic Nonlinear Schrödinger Equation on Rescaled Waveguide Manifolds",
  "authors": [
    "Bobby Wilson",
    "Xueying Yu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We use modified scattering theory to demonstrate that small-data solutions to the cubic nonlinear Schr\\\"odinger equation on rescaled waveguide manifolds, $\\mathbb{R} \\times \\mathbb{T}^d$ for $d\\geq 2$, demonstrate boundedness of Sobolev norms as well as weak instability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-15T01:13:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "cubic nonlinear schrödinger equation",
      "rescaled waveguide manifolds",
      "modified scattering",
      "weak instability",
      "sobolev norms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}