40 citations · 190 across the 39 of their papers we have counts for
7 papers · 1 filter
Recovery of a spatially-dependent coefficient from the NLS scattering map
Jason Murphy
We follow up on work of Strauss, Weder, and Watanabe concerning scattering and inverse scattering for nonlinear Schrödinger equations with nonlinearities of the form .
Threshold solutions for the 3d cubic-quintic NLS
Alex H. Ardila, Jason Murphy
We study the cubic-quintic NLS in three space dimensions. It is known that scattering holds for solutions with mass-energy in a region corresponding to positive virial, the boundar…
Recovery of a cubic nonlinearity for the nonlinear Schrödinger equation
Christopher C. Hogan, Jason Murphy, David Grow
We consider the problem of recovering a spatially-localized cubic nonlinearity in a nonlinear Schrödinger equation in dimensions two and three. We prove that solutions with data gi…
The scattering map determines the nonlinearity
Rowan Killip, Jason Murphy, Monica Visan
Using the two-dimensional nonlinear Schrödinger equation (NLS) as a model example, we present a general method for recovering the nonlinearity of a nonlinear dispersive equation fr…
Averaging for the dispersion-managed NLS
Luccas Campos, Jason Murphy, Tim Van Hoose
We establish global-in-time averaging for the -critical dispersion-managed nonlinear Schrödinger equation in the fast dispersion management regime. In particular, in the case…
Threshold solutions for the intercritical inhomogeneous NLS
Luccas Campos, Jason Murphy
We consider the focusing inhomogeneous nonlinear Schrödinger equation in , \begin{equation} i\partial_t u + Δu + |x|^{-b}|u|^{2}u=0,{equation} where $0 < b <\tfr…
Global dynamics below excited solitons for the non-radial NLS with potential
Satoshi Masaki, Jason Murphy, Jun-ichi Segata
We consider the global dynamics of solutions to the cubic nonlinear Schrödinger equation in the presence of an external potential, in the setting in which the equation admits…