Dislocation equation for a two-dimensional triangular crystal

Abstract A dislocation equation has been derived rigorously for a two-dimensional triangular crystal. The equation only relates to atoms on the borders through which two perfect crystals match together, and can be used to calculate the core configuration of a dislocation. Frenkel–Kontorova equation that is proposed phenomenologically is recovered as a truncated approximation for the sum term in the equation.