A Scattering Theory Construction of Dynamical Solitons in 3D
Abstract
Abstract We study the energy critical wave equation in three 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 ( $$i_+$$ i + ), provided the data on null infinity ( $$\mathcal {I}$$ I ) decay polynomially. Moreover, the solutions we construct are conormal on a compact manifold, the interior of which is Minkowski space. The methods of proof also extend to some energy supercritical modifications of the equation.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Annales Henri Poincaré
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 3 July 2026
- Language
- EN