A dislocation equation was derived, for a 2-dimensional triangular crystal, which applied only to atoms on the borders across which 2 perfect crystals matched together. It could be used to calculate the core configuration of a dislocation. A Frenkel-Kontorova phenomenological equation was recovered as a truncated approximation to the sum term in the equation.

Dislocation Equation for a Two-Dimensional Triangular Crystal. S.Wang: Physics Letters A, 2001, 287[3-4], 268-72