40 citations · 190 across the 39 of their papers we have counts for
46 papers
Scattering and nonlinear recovery for the 1 NLW with localized nonlinearity
Luccas Campos, Jason Murphy, Renzo Scarpelli
We consider the wave equation in 1 with a spatially-localized cubic nonlinearity. We establish scattering in a weighted space and demonstrate the injectivity of the scattering m…
Threshold dynamics for the 3 radial NLS with combined nonlinearity
Alex H. Ardila, Jason Murphy, Jiqiang Zheng
We consider the nonlinear Schrödinger equation with focusing quintic and defocusing cubic nonlinearity in three space dimensions: \[ (i\partial_t+Δ)u = |u|^2 u - |u|^4 u. \] In [18…
Stability estimates for the recovery of the nonlinearity from scattering data
Gong Chen, Jason Murphy
We prove stability estimates for the problem of recovering the nonlinearity from scattering data. We focus our attention on nonlinear Schrödinger equations of the form \[ (i\partia…
Recovery of the nonlinearity from the modified scattering map
Gong Chen, Jason Murphy
We consider a class of one-dimensional nonlinear Schrödinger equations of the form \[ (i\partial_t+Δ)u = [1+a]|u|^2 u. \] For suitable localized functions , such equations admit…
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…
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…
Asymptotic stability of solitary waves for the NLS with an attractive delta potential
Satoshi Masaki, Jason Murphy, Jun-ichi Segata
We consider the one-dimensional nonlinear Schrödinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation admits a one-parameter family o…
Cubic-quintic NLS: scattering beyond the virial threshold
Rowan Killip, Jason Murphy, Monica Visan
We consider the nonlinear Schrödinger equation in three space dimensions with combined focusing cubic and defocusing quintic nonlinearity. This problem was considered previously by…
Scattering below the ground state for the intercritical non-radial inhomogeneous NLS
Mykael Cardoso, Luiz Gustavo Farah, Carlos M. Guzmán +1
We consider the focusing inhomogeneous nonlinear Schrödinger equation \[ i\partial_t u + Δu + |x|^{-b}|u|^αu = 0\quad\text{on}\quad\mathbb{R}\times\mathbb{R}^N, \] with ,…
Scattering for the non-radial inhomogeneous NLS
Changxing Miao, Jason Murphy, Jiqiang Zheng
We extend the result of Farah and Guzmán on scattering for the cubic inhomogeneous NLS to the non-radial setting. The key new ingredient is a construction of scattering soluti…
Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations
Jason Murphy, Kenji Nakanishi
We consider nonlinear Schrödinger equations with either power-type or Hartree nonlinearity in the presence of an external potential. We show that for long-range nonlinearities, sol…
Scattering below the ground state for the 2 radial nonlinear Schrödinger equation
Anudeep Kumar Arora, Benjamin Dodson, Jason Murphy
We revisit the problem of scattering below the ground state threshold for the mass-supercritical focusing nonlinear Schrödinger equation in two space dimensions. We present a simpl…
Numerical simulations for the energy-supercritical nonlinear wave equation
Jason Murphy, Yanzhi Zhang
We carry out numerical simulations of the defocusing energy-supercritical nonlinear wave equation for a range of spherically-symmetric initial conditions. We demonstrate numericall…