The dislocation equation as a generalization of Peierls equation

A fundamental equation is derived for the structure of dislocations in solids. With the interaction potential that can be obtained properly from the first principle, the equation provides a complete basis for a comprehensive study of the dislocation structure. In particular, the full structural feature and related properties of dislocation can be predicted theoretically, which makes it possible to compare precisely the theoretical results and what is produced by experiments or numerical simulations.