Abstract
We construct new class of regular soliton solutions of the gauged planar Skyrme model on the target space $S^2$ with fractional topological charges in the scalar sector. These field configurations represent Skyrmed vortices, they have finite energy and carry topologically quantized magnetic flux $\Phi=2\pi n$ where $n$ is an integer. Using a special version of the product ansatz as guide, we obtain by numerical relaxation various multimeron solutions and investigate the pattern of interaction between the fractionally charged solitons. We show that, unlike the vortices in the Abelian Higgs model, the gauged merons may combine short range repulsion and long range attraction. Considering the strong gauge coupling limit we demonstrate that the topological quantization of the magnetic flux is determined by the Poincar\'{e} index of the planar components $\phi_\perp = \phi_1+i\phi_2$ of the Skyrme field.
Highlights
The past two decades have seen remarkable progress in our understanding of various soliton solutions in nonlinear systems
Considering the strong gauge coupling limit, we demonstrate that the topological quantization of the magnetic flux is determined by the Poincareindex of the planar components φ⊥ 1⁄4 φ1 þ iφ2 of the Skyrme field
These spatially localized field configurations arise in many different areas of physics, e.g., physics of condensed matter [1,2], solid state physics [3], nonlinear optics [4], biophysics [5], field theory [6], cosmology [7], and other disciplines. This development has sparked a lot of interest in the mathematical investigation of nonlinear systems, the fascinating techniques developed in this area of modern theoretical physics, find many other applications
Summary
We construct a new class of regular soliton solutions of the gauged planar Skyrme model on the target space S2 with fractional topological charges in the scalar sector. These field configurations represent Skyrmed vortices; they have finite energy and carry topologically quantized magnetic flux Φ 1⁄4 2πn, where n is an integer. Using a special version of the product ansatz as a guide, we obtain by numerical relaxation various multimeron solutions and investigate the pattern of interaction between the fractionally charged solitons. Considering the strong gauge coupling limit, we demonstrate that the topological quantization of the magnetic flux is determined by the Poincareindex of the planar components φ⊥ 1⁄4 φ1 þ iφ of the Skyrme field
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