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

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