{
  "id": "2106.01106",
  "version": "v1",
  "published": "2021-06-02T12:14:29.000Z",
  "updated": "2021-06-02T12:14:29.000Z",
  "title": "On Existence and Uniqueness of Asymptotic $N$-Soliton-Like Solutions of the Nonlinear Klein-Gordon Equation",
  "authors": [
    "Xavier Friederich"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We are interested in solutions of the nonlinear Klein-Gordon equation (NLKG) in $\\mathbb{R}^{1+d}$, $d\\ge1$, which behave as a soliton or a sum of solitons in large time. In the spirit of other articles focusing on the supercritical generalized Korteweg-de Vries equations and on the nonlinear Schr{\\\"o}dinger equations, we obtain an $N$-parameter family of solutions of (NLKG) which converges exponentially fast to a sum of given (unstable) solitons. For $N = 1$, this family completely describes the set of solutions converging to the soliton considered; for $N\\ge 2$, we prove uniqueness in a class with explicit algebraic rate of convergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-02T12:14:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear klein-gordon equation",
      "soliton-like solutions",
      "uniqueness",
      "asymptotic",
      "explicit algebraic rate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}