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. D66, 041701(R) (2002)] that certain modification of the ordinary model results in system which supports stable topological solitons (Hopfions) for some values of the parameters of the model. We expand the search for stability into 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.