Jesse Gell-Redman

We prove a small data scattering result for the nonlinear Schrödinger equation on asymptotically conic (scattering) manifolds, in particular on Euclidean space. For sufficiently small smooth functions prescribing incoming data on the sphere at infinity, we prove the existence of standing waves, i.e. solutions to Δu + k2u + |u|p-1u= 0 which have the same formal expansion at infinity to leading order as their analogues do in the linear case.

This is joint work with Andrew Hassell, Jacob Shapiro, and Junyong Zhang.