On the dynamics of kink-type solitons in an elastic medium

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.