A. Soffer

Modified Scattering and Asymptotics for Perturbed One-Dimensional Cubic NLS

We study the long-time dynamics of small solutions to the one-dimensional nonlinear Schr\"odinger equation \[ i\partial_t v+\partial_x^2v-\beta\abs{v}^2v +\cW(x)\abs{v}^4v+\gamma i\partial_xv=0, \] where $\cW$ is spatially localized. The cubic nonlinearity is long range and produces the logarithmic phase correction, wh...