Energy scattering for Schrödinger equation with exponential nonlinearity in two dimensions (Q1951096)

Summary: 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 \((e^{\lambda|u|^2} - 1)u\), where \(0 < \lambda < 4\pi\).