Fig. 2: Structural stability of Hopf solitons.
From: Geometric transformation and three-dimensional hopping of Hopf solitons
a–b Structural stability diagrams of LC Hopf solitons in the bulk (a) and within a confined volume with perpendicular BC and \(d=3{p}_{0}\) (b). The data points are colored based on the stability of Hopf solitons, and the contour lines of background mid-plane cone angle \({\theta }_{c}\) are shown on each diagram. \({{{{{\boldsymbol{n}}}}}}({{{{{\boldsymbol{r}}}}}})\) of labeled data points in (a–b) are shown in (d–f). c Structural stability diagram of magnetic Hopf solitons in a confined volume with perpendicular BC and \(d=3\lambda\). d–f, Preimages and director fields of representative Hopf solitons in a uniform (d), helical (e), and conical background (f), respectively. Preimages and vectors are colored based on the color scheme shown in Fig. 1d.
