{
  "id": "1703.01901",
  "version": "v1",
  "published": "2017-03-02T07:21:14.000Z",
  "updated": "2017-03-02T07:21:14.000Z",
  "title": "Ground states and energy asymptotics of the nonlinear Schrödinger equation",
  "authors": [
    "Xinran Ruan"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study analytically the existence and uniqueness of the ground state of the nonlinear Schr\\\"{o}dinger equation (NLSE) with a general power nonlinearity described by the power index $\\sigma\\ge0$. For the NLSE under a box or a harmonic potential, we can derive explicitly the approximations of the ground states and their corresponding energy and chemical potential in weak or strong interaction regimes with a fixed nonlinearity $\\sigma$. Besides, we study the case where the nonlinearity $\\sigma\\to\\infty$ with a fixed interaction strength. In particular, a bifurcation in the ground states is observed. Numerical results in 1D and 2D will be reported to support our asymptotic results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-02T07:21:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35P30",
      "35Q55",
      "65N25"
    ],
    "keywords": [
      "ground state",
      "nonlinear schrödinger equation",
      "energy asymptotics",
      "general power nonlinearity",
      "strong interaction regimes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}