  Stripe domains are narrow, elongated, reversed regions that exist in magnetic
materials with perpendicular magnetic anisotropy. Stripe domains appear as a
pair of domain walls that can exhibit topology with a nonzero chirality. Recent
experimental and numerical investigations identify an instability of stripe
domains in the long direction as a means of nucleating isolated magnetic
skyrmions. Here, the onset and nonlinear evolution of transverse instabilities
for a dynamic stripe domain known as the bion stripe are investigated. Both
non-topological and topological variants of the bion stripe are shown to
exhibit a long-wavelength transverse instability with different characteristic
features. In the former, small transverse variations in the stripe's width lead
to a neck instability that eventually pinches the non-topological stripe into a
chain of two-dimensional breathers composed of droplet soliton pairs. In the
latter case, small variations in the stripe's center results in a snake
instability whose topological structure leads to the nucleation of dynamic
magnetic skyrmions and antiskyrmions as well as perimeter-modulated droplets.
Quantitative, analytical predictions for both the early, linear evolution and
the long-time, nonlinear evolution are achieved using an averaged Lagrangian
approach that incorporates both exchange (dispersion) and anisotropy
(nonlinearity). The method of analysis is general and can be applied to other
filamentary structures.
