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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics