Stability of topological solitons in modified two-component Ginzburg-Landau model

We study the stability of Hopfions embedded in a certain modification Ginzburg-Landau model of two equally charged condensates. It has been shown by Ward [Phys. Rev. D 66, 041701(R) (2002)] that a certain modification of the ordinary model results in a system which supports stable topological solitons (Hopfions) for some values of the parameters of the model. We expand the search for stability into a previously uninvestigated region of the parameter space, charting an approximate shape for the stable/unstable boundary and find that, within the accuracy of the numerical methods used, the energy of the stable knot at the boundary is independent of the parameters.