Features of propagation and interaction of one-dimensional topological solitons in crystals

In the present work the interaction of two similar solitons (Frenkel-Kontorova dislocations) has been considered at their combined motion at the same speed in one gliding plane.Based on a numerical experiment for soliton solutions of the nonlinear sinus- Gordon wave equation,the following results were obtained: the interaction between the dislocations proved important at low velocities; the displacement field of some given dislocation was strongly distorted under the action of neighboring dislocation. In our opinion, in this case a transverse slide of the dislocation in question is observed. The interaction force between these dislocations decreases with increasing velocity and in the limit when the dislocation velocity tends to the velocity of sound,the interaction between the dislocations tends to zero. It was then obtained that the behavior of dislocation motion depended upon the height of periodical potential barrier of crystal lattice.In case of low barriers the motion is translational.In high barrier crystals the dislocation as if executes oscillating motion in the direction of slide. The tail-end ranges of dislocations are distorted.The width of dislocation periodically changes remaining all the time less than that in low barrier crystals.