We consider a complex Ginzburg-Landau equation that contains a Schrodinger term and a damping term that is proportional to the time derivative. Given well-prepared initial conditions that correspond to quantized vortices, we establish the vortex motion law until collision time.
Kurzke, M., Melcher, C., Moser, R., & Spirn, D. (2009). Dynamics for Ginzburg-Landau vortices under a mixed flow. Indiana University Mathematics Journal, 58(6), 2597-2621. https://doi.org/10.1512/iumj.2009.58.3842