Existence of Non-Topological Solitons in the Self-Dual Chern-Simons Theory

摘要

In the recently discovered (2+1)-dimensional relativistic Chern-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 nontopological vortex-like solutions in R(sup 2) but the latter have been rather elusive to a rigorous construction. The main purpose in the paper is to prove the existence of non-topological radially symmetric N-vortex solutions in the self-dual Chern-Simons model. By a shooting method, one obtains a continuous family of gauge-distinct N-vortex solutions. Moreover, one is also able to classify all possible bare (or 0-vortex) solutions.