Energy scattering for Schrödinger equation with exponential nonlinearity in two dimensions. (English) Zbl 1264.35233
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 \(0 < \lambda < 4\pi\).
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35P25 | Scattering theory for PDEs |
| 81U05 | \(2\)-body potential quantum scattering theory |
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