Asymptotic Behavior of the Nonlinear Schrödinger Equation with Harmonic Trapping
Asymptotic Behavior of the Nonlinear Schrödinger Equation with Harmonic Trapping
Abstract We consider the cubic nonlinear Schrödinger equation with harmonic trapping on ℝ D (1 ≤ D ≤ 5). In the case when all directions but one are trapped (aka “cigar‐shaped trap”), we prove modified scattering and construct modified wave operators for small initial and final data, respectively. The asymptotic …