Published: April 11, 2018

Stripe solitons are long solitary wave filaments which can be found in a variety of multidimensional contexts, e.g., in shallow water waves, Bose-Einstein condensates, and ferromagnetic materials. In a recent paper published in Physical Review B, a theory for modulations of a two-dimensional magnetic soliton filament, known as the bion stripe, is presented. The bion stripe is a localized wave in one spatial direction where the out-of-plane magnetization is almost reversed with respect to its environment. In the other, transverse spatial direction, the bion stripe is directly elongated/extended as a soliton filament.  The bion stripe is uniquely characterized by its in-plane precessional frequency. Depending on the sign of the frequency, the bion stripe can be classified as topological (negative) or non-topological (positive). It is found that the bion stripe is unstable to long wavelength perturbations along the transverse, extension direction. Furthermore, the characteristic wavelength and growth rate of the instability is determined. Interestingly, the form of the instability is determined by the topological structure of the bion stripe, as the topological bion stripe exhibits a "snake" instability and the non-topological stripe exhibits a "neck” instability. The snake and neck instabilities are familiar from well-known transverse instabilities in other soliton-supporting media such as Bose-Einstein condensates and nonlinear optics. This paper was co-authored by Dispersive Hydrodynamics Lab members Max Ruth, Ezio Iaccoca, and Mark Hoefer in collaboration with Panos Kevrekidis at the University of Massachusetts, Amherst.