  Analysis of the nonlinear Schrodinger 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 Schrodinger equation and provide several
interesting properties of the reconnection process, in particular the
non-singular 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
analytical 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.
