Energy Scattering for Schrödinger Equation with Exponential Nonlinearity in Two Dimensions. (9th April 2013) - Wang, Shuxia
Abstract : When the spatial dimensionsn = 2, the initial datau 0 ∈ H 1, and the HamiltonianH ( u 0 ) ≤ 1, we prove that the scattering operator is well defined in the whole energy spaceH 1 ( ℝ 2 ) for nonlinear Schrödinger equation with exponential nonlinearity( e λ | u | 2 - 1 ) u, where0 < λ < 4 π .