Energy Scattering for Schrödinger Equation with Exponential Nonlinearity in Two Dimensions

Details Energy Scattering for Schrödinger Equation with Exponential Nonlinearity in Two Dimensions Energy Scattering for Schrödinger Equation with Exponential Nonlinearity in Two Dimensions

2011-04-23

arxiv.org/abs/1104.4540v8

Mathematics

Analysis of PDEs

20 pages

Scientific paper

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
Schr\"{o}dinger equation with exponential nonlinearity $(e^{\lambda|u|^2}-1)u$,
where $0<\lambda<4\pi$.

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