Breathing vortex solitons in nonrelativistic Chern-Simons gauge theory

We present exact solutions for breather solitons in the (2+1)-dimensional Chern-Simons gauge theory with external magnetic field B. The breather soliton is a time-dependent solution whose size is oscillating and whose center of mass moves ina cyclotron motion. These solitions describe how the Jackiw-Pi solitons behave in the external magnetic field. We then apply the Bohr-Sommerfeld semiclassical quantization to the breathing mode and the cyclotron motion. It is found that the orbital angular momentum takes on an integer value and that the quantum soliton is in the Landau level.