{
  "id": "2307.00980",
  "version": "v1",
  "published": "2023-07-03T12:54:00.000Z",
  "updated": "2023-07-03T12:54:00.000Z",
  "title": "Variational problems for the system of nonlinear Schrödinger equations with derivative nonlinearities",
  "authors": [
    "Hiroyuki Hirayama",
    "Masahiro Ikeda"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We consider the Cauchy problem of the system of nonlinear Schr\\\"odinger equations with derivative nonlinearlity. This system was introduced by Colin-Colin (2004) as a model of laser-plasma interactions. We study existence of ground state solutions and the global well-posedness of this system by using the variational methods. We also consider the stability of traveling waves for this system. These problems are proposed by Colin-Colin as the open problems. We give a subset of the ground-states set which satisfies the condition of stability. In particular, we prove the stability of the set of traveling waves with small speed for $1$-dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-03T12:54:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "nonlinear schrödinger equations",
      "variational problems",
      "derivative nonlinearities",
      "ground state solutions",
      "traveling waves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}