58 citations · 278 across the 41 of their papers we have counts for
6 papers · 2 filters
Global well-posedness for the cubic nonlinear Schr{ö}dinger equation with initial lying in -based Sobolev spaces
Benjamin Dodson, Avraham Soffer, Thomas Spencer
In this paper we continue our study [DSS20] of the nonlinear Schrödinger equation (NLS) with bounded initial data which do not vanish at infinity. Local well-posedness on $\mathbb{…
Instability of the soliton for the focusing, mass-critical generalized KdV equation
Benjamin Dodson, Cristian Gavrus
In this paper we prove instability of the soliton for the focusing, mass-critical generalized KdV equation. We prove that the solution to the generalized KdV equation for any initi…
The sequential convergence of a solution to the one dimensional, mass-critical NLS above the ground state
Benjamin Dodson
In this paper we generalize a weak sequential result of \cite{fan20182} to any non-scattering solutions in one dimension. No symmetry assumptions are required for the initial data.
Spacetime integral bounds for the energy-critical nonlinear wave equation
Benjamin Dodson
In this paper we prove a global spacetime bound for the quintic, nonlinear wave equation in three dimensions. This bound depends on the and $L_{t}^{\inft…
Global well-posedness for the defocusing, cubic nonlinear Schr{ö}dinger equation with initial data in a critical space
Benjamin Dodson
In this note we prove global well-posedness for the defocusing, cubic nonlinear Schr{ö}dinger equation with initial data lying in a critical Sobolev space.
The nonlinear Schrodinger equation on Z and R with bounded initial data: examples and conjectures
Benjamin Dodson, Avraham Soffer, Thomas Spencer
We study the nonlinear Schrödinger equation (NLS) with bounded initial data which does not vanish at infinity. Examples include periodic, quasi-periodic and random initial data. On…