6 papers · 1 filter
Well-posedness and blowup for the dispersion-managed nonlinear Schrödinger equation
Jason Murphy, Tim Van Hoose
We consider the nonlinear Schrödinger equation with periodic dispersion management. We first establish global-in-time Strichartz estimates for the underlying linear equation with s…
Modified scattering for a dispersion-managed nonlinear Schrödinger equation
Jason Murphy, Tim Van Hoose
We prove sharp decay and modified scattering for a one-dimensional dispersion-managed cubic nonlinear Schrödinger equation with small initial data chosen from a weighted…
Threshold scattering for the 2d radial cubic-quintic NLS
Jason Murphy
We consider the cubic-quintic nonlinear Schrödinger equation in two space dimensions. For this model, X. Cheng established scattering for data with mass strictly below that o…
Threshold scattering for the focusing NLS with a repulsive potential
Changxing Miao, Jason Murphy, Jiqiang Zheng
We adapt the arguments in the recent work of Duyckaerts, Landoulsi, and Roudenko to establish a scattering result at the sharp threshold for the focusing cubic NLS with a repu…
Scattering for the non-radial energy-critical inhomogeneous NLS
Carlos M. Guzmán, Jason Murphy
We prove scattering below the ground state threshold for an energy-critical inhomogeneous nonlinear Schrödinger equation in three space dimensions. In particular, we extend results…
A simple proof of scattering for the intercritical inhomogeneous NLS
Jason Murphy
We adapt the argument of Dodson-Murphy to give a simple proof of scattering below the ground state for the intercritical inhomogeneous nonlinear Schrödinger equation. The decaying…