THE EXISTENCE OF NONTOPOLOGICAL SOLITONS IN THE SELF-DUAL CHERN-SIMONS THEORY

In the recently discovered (2 + 1)-dimensional relativistic Chem-Simons model, self-duality can be achieved when the Higgs potential density assumes a special form for which both the asymmetric and symmetric vacua are ground state solutions. This important feature may imply the coexistence of static topological and non-topological vortex-like solutions in R2 but the latter have been rather elusive to a rigorous construction. Our main purpose in this paper is to prove the existence of non-topological radially symmetric N-vortex solutions in the self-dual Chem-Simons model. By a shooting method, we obtain a continuous family of gauge-distinct N-vortex solutions. Moreover, we are also able to classify all possible bare (or 0-vortex) solutions.