Time-dependent topological Chern-Simons solitons in external magnetic field

We present a new method to construct time-dependent periodic solutions using static solutions in the (2+1)-dimensional Chern-Simons gauge theory with external magnetic field B. We apply this method to vortex solitons, which may be topological or nontopological; topological vortices are identified with Laughlins quasiparticles or quasiholes in the fractional quantum Hall effect. Our periodic solution represents that vortex solitons make cyclotron motion. After applying the Bohr-Sommerfeld semiclassical quantization, it is found that the quantum soliton is in the Landau level.