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A Global Wavefront Set Condition for Defining Bony's Paraproduct Decomposition
Josh Mott, Tim Van Hoose
We establish a natural generalization of the Hörmander condition for the multiplication of Besov distributions using the global wavefront set framework of Coriasco, Johansson, and…
On Analyticity of Solitons for the Periodic Dispersion-Managed Nonlinear Schrödinger Equation
Sebastian Herr, Dirk Hundertmark, Jeremy L. Marzuola +1
We explore the regularity of energy maximizers for the Lagrangian of a periodic dispersion managed fiber optic at fixed intensity, on a torus of length and with vanishing avera…
Modified Scattering for the Hartree Nonlinear Schrödinger Equation
Tim Van Hoose
We prove sharp decay and modified scattering for the Hartree nonlinear Schrödinger equation in dimensions and using the testing by wavepackets method of Ifrim an…
Modified Scattering for the Schrödinger-Bopp-Podolsky Equation
Tim Van Hoose
We prove sharp decay and modified scattering for the Schrödinger-Bopp-Podolsky equation in and spatial dimensions with small initial data chosen from a weighted…
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…
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…