Edge dislocations in crystal structures considered as traveling waves in discrete models

The static stress needed to depin a 2D edge dislocation, the lower dynamic stress needed to keep it moving, its velocity, and displacement vector profile are calculated from first principles. We use a simplified discrete model whose far field distortion tensor decays algebraically with distance as in the usual elasticity. Dislocation depinning in the strongly overdamped case (including the effect of fluctuations) is analytically described. N parallel edge dislocations whose average interdislocation distance divided by the Burgers vector of a single dislocation is L>>1 can depin a given one if N=O(L). Then a limiting dislocation density can be defined and calculated in simple cases.