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Here we study the instability of the vortex motion caused by non-monotonous dependence of the friction force on the vortex velocity in the presence of a gyroforce. The analysis is done within the frameworks of “minimal” model for the elastic string subject to friction force and gyroforce. We demonstrate that even a weak gyroforce renders the condition for onset of instability more strict than for a vortex not subject to gyroforce: either the friction force must exceed a threshold, or its non-monotonic velocity dependence must be a rather steep function.

The question of kink-type (domain-wall-type) topological soliton motion with a kink interaction with the elastic deformation field was considered. The viscosity of the deformation field was taken into account. It is shown that kink motion with a velocity in some interval around the sound velocity is impossible for some relations between the system parameters (elastic gap effect). For small coupling constants or a large viscosity the elastic gap does not exist. The results can describe the domain wall dynamics in magnetics or the proton kink dynamics in systems with hydrogen bounds.

The dynamical properties of topological precessional solitons in two-dimensional ferromagnets with uniaxial anisotropy are considered. It turns out that free (without external forces acting) soliton motion corresponds to some rotary motion (analogous to Larmor precession of a charged particle in an external magnetic field). The effective mass of the soliton is found. It is shown that the denominator of the mass value contains the anisotropy constant, so in the isotropic ferromagnet the topological soliton motion is impossible.