Dynamics of quasi-1D topological soliton in 2D strongly anisotropic crystal

We investigate a 2D strongly anisotropic crystal: 2D system of coupled linear chains of particles with strong intrachain and weak interchain interactions: a generalization of the Frenkel-Kontorova (FK) model giving better approximation to polymer crystals consisting of all moving chains. We study shape and dynamics of topological solitons located mainly on one chain of the crystal. It turns out that at weak interactions between chains there exist exact propagating soliton-like solutions. We have found that the upper boundary of their velocity spectrum is less than unity (the upper boundary of soliton velocity spectrum in the corresponding FK model). The reason of this new restriction is appearance of Cherenkov-type radiation emitted by the kinks moving at higher velocities. In the case of stronger interchain interactions the exact soliton-like solutions are absent. Kinks emit phonons at any velocity. This emission originates from resonances between the kink and phonon modes touched in the second or the third Brillouin zones and so this effect is a pure result of discreteness of the crystal. Deceleration of kink falls exponentially with its velocity (as in the FK model) at medium velocities and is nonzero constant at low velocities (contrary to the FK model where deceleration at low velocities is zero), so at all velocities there is no generally expected direct proportion between deceleration and velocity. Spatial pattern of phonons emitted proves to be in accordance with the conception that kink emits packets of corresponding resonant phonons in direction of their group velocities.