{
  "id": "2408.14269",
  "version": "v1",
  "published": "2024-08-26T13:45:13.000Z",
  "updated": "2024-08-26T13:45:13.000Z",
  "title": "A New Paradigm For Scattering Theory of Linear And Nonlinear Waves: Review And Open Problem",
  "authors": [
    "Avy Soffer"
  ],
  "comment": "73 pages, to appear",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.PS",
    "quant-ph"
  ],
  "abstract": "I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent potentials, as well as NLS, NLKG, and NLW equations. Additionally, I discuss a series of open problems, along with their significance and potential future applications in scattering and inverse scattering.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-26T13:45:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "open problem",
      "scattering theory",
      "nonlinear waves",
      "equations encompass time-dependent potentials",
      "general interaction terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 73,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}