The 1-dimensional Frenkel-Kontorova model was generalized in order to describe topological point defects and dislocations in anisotropic crystals of higher dimensions. The main modification was that a substrate periodic potential in the model was not considered to be an imposed spatially periodic force, but was constructed in a self-consistent manner such that any disturbance in one of the chains caused a violation of spatial periodicity in the adjacent chains. Static and moving soliton (kink and anti-kink) solutions were found numerically for 2-dimensional and 3-dimensional anisotropic crystals. Bound states of kink-antikink and kink-kink (antikink-antikink) pairs, and their dynamic properties, were studied. Arrays of soliton states were shown to form dislocations of edge type, and their deformation energy distribution on the crystal lattice was calculated.

Topological Solitons and Dislocations in Two- and Three-Dimensional Anisotropic Crystals P.L.Christiansen, A.V.Savin, A.V.Zolotaryuk: Physical Review B, 1998, 57[21], 13564-72