  The changes observed in the topology of superfluid helium vortices have
intrigued people for some time now [1]. These vortices either extend from wall
to wall, however tangled they may be in between, or else can be roughly
circular and freely move around the superfluid [1]. Some time ago, Richard
Feynman postulated that two oppositely polarized line vortices could, if they
cross at two points, reconnect so as to create a circular vortex that snaps off
and subsequently lives a life of its own [2]. This is often simply postulated
in numerical experiments, e.g. [1], [3]. That an opposite line vortex pair
solution of the Nonlinear Schrodinger equation (NLS) for HeII is unstable has
been demonstrated theoretically [4]. Reconnection at a point has been obtained
numerically [5]. What remained to prove was that known, stationary, double
vortex line solutions can thus reproduce one of the one parameter solitonic
family of solutions for circular vortices as found for NLS [6]. In other words,
can this reconnection really lead to a full confirmation of Feynman's
hypothesis? Our first step was a similar changeover calculation for a limiting
case, unfortunately such that the vortex configuration was degenerate [7], [8].
However, surprisingly complete dynamic changeover from cylindrical to spherical
symmetry of the soliton was observed in [7]. This augured well for the present
effort.
