7 papers
Scattering in spacetime cones for the nonlinear Schrödinger equation
Andrew Hassell, Qiuye Jia, Xiaoxu Wu
We consider the nonlinear Schrödinger equation on , with a class of `mixed' nonlinearities that admit soliton solutions. We are interested in the long-time behavi…
Lecture notes on non-elliptic Fredholm theory
Andrew Hassell, Qiuye Jia, Ethan Sussman
These are lecture notes from the Austral Winter School on Microlocal Analysis and Non-elliptic Fredholm Theory, held at the Australian National University, Canberra, June 30 -- Jul…
The scattering map for the Schrodinger operator on curved spaces
Andrew Hassell, Qiuye Jia
Let be a Schrödinger operator with metric and potential perturbation that are compactly supported in spacetime . Here and $Δ_g…
Microlocal analysis of the non-relativistic limit of the Klein--Gordon equation: Asymptotics
Andrew Hassell, Qiuye Jia, Ethan Sussman +1
This is the less technical half of a two-part work in which we introduce a robust microlocal framework for analyzing the non-relativistic limit of relativistic wave equations with…
Microlocal analysis of the non-relativistic limit of the Klein--Gordon equation: Estimates
Andrew Hassell, Qiuye Jia, Ethan Sussman +1
This is the more technical half of a two-part work in which we introduce a robust microlocal framework for analyzing the non-relativistic limit of relativistic wave equations with…
The final state problem for the nonlinear Schrodinger equation in dimensions 1, 2 and 3
Andrew Hassell, Qiuye Jia
In this article we consider the defocusing nonlinear Schrödinger equation, with time-dependent potential, in space dimensions and , with nonlinearity , …
Geodesic flow and decay of traces on hyperbolic surfaces
Antoine Gansemer, Andrew Hassell
We study pseudodifferential operators on a hyperbolic surface using `Zelditch quantization'. We motivate and study the trace of , where is a fixed operator and…