Absence of the breakdown of ferrodark solitons exhibiting a snake instability

Abstract

We investigate the dynamical stability and real time dynamics of the two-types of ferrodark solitons (FDSs) which occur as topological magnetic domain walls in the easy-plane phase of a quasi-two-dimensional (2D) ferromagnetic spin-1 Bose-Einstein condensate. The type-I FDS has positive inertial mass and exhibits a single dynamical instability that generates in plane spin winding, causing polar-core spin vortex dipoles. The positive inertial mass leads to the elastic oscillations of the soliton under transverse perturbations. The type-II FDS has negative inertial mass and exhibits a snake instability and a spin-twist instability, with the latter involving the generation of out of plane spin winding. Distinct from the normal dynamics of negative mass solitons under long wave length transverse perturbations, the snake instability does not lead to the type-II FDS breaking down. Instead, segments of the type-II FDS convert to type-I and mass vortex dipoles are produced. The resulting hybridized-chain of the two soliton types and vortices exhibits complex 2D soliton dynamics at long times while the vortices remain confined and the topological structure of a magnetic domain wall is preserved.