9 papers
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…
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…
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…
Scattering for defocusing energy subcritical nonlinear wave equations
Benjamin Dodson, Andrew Lawrie, Dana Mendelson +1
We consider the Cauchy problem for the defocusing power type nonlinear wave equation in -dimensions for energy subcritical powers in the range . We prove that…