---
res:
  bibo_abstract:
  - "We prove that solutions of the cubic nonlinear Schr\\\"odinger equation on $\\Bbb{R}^2$
    can be approximated by a finite-dimensional Hamiltonian system, uniformly on bounded
    sets of initial data. This is despite the wealth of non-compact symmetries: scaling,
    translation, and Galilei boosts.\r\n\r\nComplementing this approximation result,
    we show that all solutions of the finite-dimensional Hamiltonian system we use
    can be approximated by the full PDE.\r\n\r\nA key ingredient in these results
    is the development of a general methodology for transfering uniform global space-time
    bounds to suitable Fourier truncations of dispersive PDE models.\r\n\r\nAs an
    application, we prove symplectic non-squeezing (in the sense of Gromov) for the
    cubic NLS on $\\Bbb{R}^2$. This is the first symplectic non-squeezing result for
    a Hamiltonian PDE in infinite volume. It is also the first unconditional symplectic
    non-squeezing result in a scaling-critical setting.\r\n\r\nFinally, we discuss
    implications of non-squeezing on the nature of scattering.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Rowan
      foaf_name: Killip, Rowan
      foaf_surname: Killip
  - foaf_Person:
      foaf_givenName: Monica
      foaf_name: Visan, Monica
      foaf_surname: Visan
      foaf_workInfoHomepage: http://www.librecat.org/personId=056daca0-b8d1-11f0-964f-f91054abf8ca
  - foaf_Person:
      foaf_givenName: Xiaoyi
      foaf_name: Zhang, Xiaoyi
      foaf_surname: Zhang
  bibo_doi: 10.1353/ajm.2021.0014
  bibo_issue: '2'
  bibo_volume: 143
  dct_date: 2021^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1080-6377
  dct_language: eng
  dct_publisher: Johns Hopkins University Press@
  dct_title: Finite-dimensional approximation and non-squeezing for the cubic nonlinear
    Schrödinger equation on ℝ2@
...