Scattering for the two-dimensional NLS with exponential nonlinearity

@article{Ibrahim2012ScatteringFT,
  title={Scattering for the two-dimensional NLS with exponential nonlinearity},
  author={S. A. Hoda Ibrahim and Mohamed Majdoub and Nader Masmoudi and Kenji Nakanishi},
  journal={Nonlinearity},
  year={2012},
  volume={25},
  pages={1843 - 1849}
}
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… 

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