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In this paper we study the structure of the manifold of solitary waves insome deformations of SO(2) symmetric two-component scalar field theoreticalmodels in two-dimensional Minkowski space. The deformation is chosen in orderto make the analogous mechanical system Hamilton-Jacobi separable in polarcoordinates and displays a singularity at the origin of the internal plane. Theexistence of the singularity confers interesting and intriguing properties tothe solitary waves or kink solutions.Comment: 25 pages, 18 figure

One-dimensional solitary waves in singular deformations ofSO(2) invariant two-component scalar field theory models