Convergence to Scattering States in the Nonlinear Schrödinger Equation

Pascal Bégout

In this paper, we consider global solutions of the following nonlinear Schrödinger equation $i{u}_t+\Delta u+\lambda |u{|}^{\alpha }u=0,$ in ${\mathbb{R}}^N,$ with $\lambda \in \mathbb{R},$ $\alpha \in (0,\frac{4}{N-2})$ $(α\in(0,\infty…