A model for Hopfions on the space-time S^3*R

De Carli E., Ferreira L.A.

We construct static and time dependent exact soliton solutions for a theory of scalarfields taking values on a wide class of two dimensional target spaces, and definedon the four dimensional space-time S33R. The construction is based on an ansatzbuilt out of special coordinates on S3. The requirement for finite energy introduceboundary conditions that determine an infinite discrete spectrum of frequencies forthe oscillating solutions. For the case where the target space is the sphere S2, weobtain static soliton solutions with nontrivial Hopf topological charges. In addition,such Hopfions can oscillate in time, preserving their topological Hopf charge, withany of the frequencies belonging to that infinite discrete spectrum