Energy Scattering for Schrödinger Equation with Exponential Nonlinearity in Two Dimensions

Abstract

When the spatial dimensions $n$=2, the initial data $u_0\in H^1$ and the Hamiltonian $H(u_0)\le 1$, 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 $0<\lambda <4\pi$.

20 pages

References in corpus (3)

• Global well-posedness and scattering for the defocusing, $L^2$-critical, nonlinear Schr{ö}dinger equation when $d=2$
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case