Scattering for the two-dimensional NLS with exponential nonlinearity

S. Ibrahim, M. Majdoub, N. Masmoudi, K. Nakanishi

Research output: Contribution to journalArticle

Abstract

We investigate existence and asymptotic completeness of the wave operators for nonlinear Schrödinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We prove that if the Hamiltonian is below the critical value, then the solution approaches a free Schrödinger solution at the time infinity.

Original languageEnglish (US)
Pages (from-to)1843-1849
Number of pages7
JournalNonlinearity
Volume25
Issue number6
DOIs
StatePublished - Jun 2012

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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