One-dimensional solitary waves in singular deformations of SO(2)   invariant two-component scalar field theory models
  In this paper we study the structure of the manifold of solitary waves in some deformations of SO(2) symmetric two-component scalar field theoretical models in two-dimensional Minkowski space. The deformation is chosen in order to make the analogous mechanical system Hamilton-Jacobi separable in polar coordinates and displays a singularity at the origin of the internal plane. The existence of the singularity confers interesting and intriguing properties to the solitary waves or kink solutions. 
A. Alonso-Izquierdo, J. Mateos Guilarte