Existence of mixed type solutions in the SU(3) Chern–Simons theory in $$\mathbb {R}^2$$ R 2

Abstract

In this article, we are concerned with the SU(3) Chern–Simons theory in \(\mathbb {R}^2\). It is believed that the self-dual equations of the theory possess three types of solutions, classified according to their (spatial) limiting behaviors. Solutions corresponding to the topological and the nontopological limiting behaviors have been shown to exist in the literature under various conditions. However, solutions satisfying the third limiting behavior, which we call mixed type solutions, have not yet been shown to exist explicitly. The purpose of this article is to show the existence of these mixed type solutions in a radially symmetric situation using the variational analysis incorporated with the bubbling argument.