{
  "id": "2403.12336",
  "version": "v1",
  "published": "2024-03-19T00:52:49.000Z",
  "updated": "2024-03-19T00:52:49.000Z",
  "title": "Collision of two solitons for $1d$ Nonlinear Schrodinger Equation with same mass",
  "authors": [
    "Abdon Moutinho"
  ],
  "comment": "First version. Comments are welcome",
  "categories": [
    "math.AP",
    "math-ph",
    "math.CA",
    "math.MP"
  ],
  "abstract": "We study the global dynamics of the collision of two solitons having the same mass for one-dimensional Nonlinear Schr\\\"odinger models with multi-power nonlinearity. For any natural number k, it is verified that if the incoming speed v between the two solitary waves is small enough, then, after the collision, the two solitons will move away with an outcoming speed v_{f}=v+O(v^{k}) and the remainder of the solution will also have energy and weighted norms of order O(v^{k}). This is applied to several one-dimensional models such as the cubic NLS and the cubic-quintic NLS.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-19T00:52:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B35",
      "35B24",
      "35C11",
      "35C08"
    ],
    "keywords": [
      "nonlinear schrodinger equation",
      "cubic nls",
      "global dynamics",
      "one-dimensional models",
      "one-dimensional nonlinear"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}