It was recalled that, in the lattice theory of dislocations, the dislocation equation which included discreteness was of non-linear integro-differential type. It could hardly be solved. Here, a variational principle for the dislocation equation was presented. By using the Ritz approximation method, the variational solution was obtained, which was the same as the Peierls–Nabarro solution when the discreteness effect terms were ignored and the accurate value of the variational parameter was obtained when the discreteness effect terms were taken into account. As a natural generalization, a modified form of the sinusoidal law of force was proposed. It was found that the fine structure of the dislocation core could be predicted theoretically as long as the parameter in the modified law of force was selected properly.

Variational Principle for the Dislocation Equation in Lattice Theory. S.F.Wang, X.Z.Wu, Y.F.Wang: Physica Scripta, 2007, 76[5], 593-6