For the planar Gross-Pitaevskii equation, explicit n-vortex solutions are constructed whose dynamics follow the Helmholtz-Kirchhoff system at leading order, with the first correction given by a linear wave equation.
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Vortex dynamics for the Gross-Pitaevskii equation
For the planar Gross-Pitaevskii equation, explicit n-vortex solutions are constructed whose dynamics follow the Helmholtz-Kirchhoff system at leading order, with the first correction given by a linear wave equation.