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arXiv · 1104.4540

Energy Scattering for Schr\"{o}dinger Equation with Exponential Nonlinearity in Two Dimensions

Shuxia Wang
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Abstract

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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Shuxia Wang. 2011-04-23. Energy Scattering for Schr\"{o}dinger Equation with Exponential Nonlinearity in Two Dimensions. https://arxiv.org/abs/1104.4540

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