A scattering theory construction of dynamical solitons in 3d

Understand

We study the energy critical wave equation in 3 dimensions around a single soliton.

• We obtain energy boundedness (modulo unstable modes) for the linearised problem.
• We use this to construct scattering solutions in a neighbourhood of timelike infinity ($i_+$), provided the data on null infinity ($\scri$) decay polynomially.
• Moreover, the solutions we construct are conormal on a blow-up of Minkowski space.