A dislocation equation has been derived rigorously for a two-dimensional tr
iangular crystal. The equation only relates to atoms on the borders through
which two perfect crystals match together, and can be used to calculate th
e core configuration of a dislocation. Frenkel-Kontorova equation that is p
roposed phenomenologically is recovered as a truncated approximation for th
e sum term in the equation. (C) 2001 Published by Elsevier Science B.V.