Energy Scattering for Schrödinger Equation with Exponential Nonlinearity in Two Dimensions

When the spatial dimensions $n$=2, the initial data $u_0\in H^1$ and the Hamiltonian $H(u_0)\leq 1$, we prove that the scattering operator is well-defined in the whole energy space $H^1(\mathbb{R}^2)$ for nonlinear Schrödinger equation with exponential nonlinearity $(e^{λ|u|^2}-1)u$, where $0<λ<4π$.

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