On the asymptotic behavior of solutions for the self-dual Maxwell-Chern-Simons $ O(3) $ Sigma model

Abstract

<p style='text-indent:20px;'>In this paper, we consider the nonlinear equations arising from the self-dual Maxwell-Chern-Simons gauged <inline-formula><tex-math id="M2">\begin{document}$ O(3) $\end{document}</tex-math></inline-formula> sigma model on (2+1)-dimensional Minkowski space <inline-formula><tex-math id="M3">\begin{document}$ {\bf R^{2,1}} $\end{document}</tex-math></inline-formula> with the metric <inline-formula><tex-math id="M4">\begin{document}$ {\mathrm {diag}}(1,-1,-1) $\end{document}</tex-math></inline-formula>. We establish the asymptotic behavior of multivortex solutions corresponding to their flux and find the range of the flux for non-topological solutions. Moreover, we prove the radial symmetry property under certain conditions in one vortex point case.</p>