Dynamics of two-dimensional radiating vortices described by the nonlinear Schrödinger equation

The paper considers the dynamics of dark charged solitons (vortices) described by the two-dimensional (2D) nonlinear Schrödinger equation (NSE) with a repulsive potential. The dynamics of these point-like vortices in the NSE is quite different in comparison with the vortices in an incompressible liquid because of the possibility of wave-like emission of energy, momentum, and angular momentum in the first case. Another important feature is the characteristic scale of the problem, namely the screening parameter. Related problems of the collapse of a vortex dipole and the decay of a multicharged vortex in a region bounded by an absolutely reflecting shell are investigated both analytically and numerically. The conditions and scaling of a vortex dipole collapse and the limitations on the decay of a multicharge dipole in a bounded region are obtained.