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

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Hamiltonians
nonlinearity
Scattering
Nonlinearity
Wave Operator
defocusing
completeness
Potential energy
Kinetic energy
scattering
Nonlinear equations
infinity
nonlinear equations
Critical value
Mathematical operators
Completeness
Nonlinear Equations
kinetic energy
potential energy
Infinity

ASJC Scopus subject areas

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

Cite this

Scattering for the two-dimensional NLS with exponential nonlinearity. / Ibrahim, S.; Majdoub, M.; Masmoudi, N.; Nakanishi, K.

In: Nonlinearity, Vol. 25, No. 6, 06.2012, p. 1843-1849.

Research output: Contribution to journalArticle

Ibrahim, S. ; Majdoub, M. ; Masmoudi, N. ; Nakanishi, K. / Scattering for the two-dimensional NLS with exponential nonlinearity. In: Nonlinearity. 2012 ; Vol. 25, No. 6. pp. 1843-1849.
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