Analytical solution for nonlinear Schrödinger vortex reconnection

Analysis of the nonlinear Schrödinger vortex reconnection is given in terms of coordinate-time power series. The lowest order terms in these series correspond to a solution of the linear Schrödinger equation and provide several interesting properties of the reconnection process, in particular the nonsingular character of reconnections, the anti-parallel configuration of vortex filaments and a square-root law of approach just before/after reconnections. The complete infinite power series represents a fully nonlinear analytic solution in a finite volume which includes the reconnection point, and is valid for finite time provided the initial condition is an analytic function. These series solutions are free from the periodicity artifacts and discretization error of the direct computational approaches and they are easy to analyze using a computer algebra program.