Jinyeop Lee

Scattering Across the Long-Range Threshold for One-Dimensional Nonlinear Schr\"odinger Equations

We study small solutions to the one-dimensional nonlinear Schr\"odinger family \[ \mathrm{i}\partial_t u_\delta=-\partial_x^2u_\delta+\kappa|u_\delta|^{2+\delta}u_\delta, \qquad 0\leq\delta\leq\delta_0, \] uniformly as $\delta\to0^+$ and $t\to\infty$, across the threshold between cubic modified scattering and nearby-po...