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

Abstract

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.

arXiv comment25 pages, 18 figures

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• Geometric Construction of non-linear Sigma models with Q-ball/Q-kink solutions
• Topological and non-topological kink families in non-linear $({\mathbb{S}}^1\times {\mathbb{S}}^1)$-Sigma models