{
  "annotation_id": "ddda4a55-3fe6-459c-a4c2-e36cd4e5cd4b",
  "date_created": "2026-02-17T05:53:12.063000Z",
  "date_modified": "2026-02-17T05:53:12.063000Z",
  "file_hash": "d52ac94944cc4e8f60c9722a4bc8d438becaeb0f12b60b1591d20bcb92dff1d2",
  "private": false,
  "record": {
    "abstract": "We study the Calogero--Moser derivative nonlinear Schr\\\"odinger equation (CM-DNLS), a mass-critical and completely integrable dispersive model. Recent works established finite-time blow-up constructions and soliton resolution, describing the asymptotic behaviors of blow-up solutions.\n  In this paper, we go beyond soliton resolution and provide a sharp classification of finite-time blow-up dynamics in the \\textit{single-bubble} regime. Assuming that a solution blows up at time $0\u003cT\u003c\\infty$ with a single-soliton profile, we determine all possible blow-up rates. For initial data in $H^{2L+1}(\\mathbb{R})$ with $L\\ge1$, we prove a dichotomy: either the solution lies in a \\emph{quantized regime}, where the scaling parameter satisfies \\[\n  \\lambda(t)\\sim (T-t)^{2k},\\qquad 1\\le k\\le L, \\] with convergent phase and translation parameters, or it lies in an \\emph{exotic regime}, where the blow-up rate satisfies $\\lambda(t)\\lesssim (T-t)^{2L+\\frac 32}$. To our knowledge, this is the first classification result for quantized blow-up dynamics in the class of dispersive models. We provide a framework for identifying the quantized blow-up rates in classification problems.\n  The proof relies on a modulation analysis combined with the hierarchy of conservation laws provided by the complete integrability of (CM-DNLS). However, it does not use \\emph{more refined integrability-based techniques}, such as the inverse scattering method, the method of commuting flows, or the explicit formula. As a result, our analysis applies beyond the chiral solutions.",
    "arxiv_id": "2601.07410",
    "authors": [
      "Uihyeon Jeong",
      "Kihyun Kim",
      "Taegyu Kim",
      "Soonsik Kwon"
    ],
    "categories": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "title": "Classification of single-bubble blow-up solutions for Calogero--Moser derivative nonlinear Schr\\\"odinger equation",
    "url": "https://arxiv.org/abs/2601.07410",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4485402b-e439-4d0c-af39-20044676e5b5",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}