  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. The methods of proof also extend to some
energy supercritical modifications of the equation.
