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The static stress needed to depin a 2D edge dislocation, the lower dynamicstress needed to keep it moving, its velocity and displacement vector profileare calculated from first principles. We use a simplified discrete model whosefar field distortion tensor decays algebraically with distance as in the usualelasticity. An analytical description of dislocation depinning in the stronglyoverdamped case (including the effect of fluctuations) is also given. A set of$N$ parallel edge dislocations whose centers are far from each other can depina given one provided $N=O(L)$, where $L$ is the average inter-dislocationdistance divided by the Burgers vector of a single dislocation. Then a limitingdislocation density can be defined and calculated in simple cases.Comment: 10 pages, 3 eps figures, Revtex 4. Final version, corrected minor  error

Edge Dislocations in Crystal Structures Considered as Traveling Waves in Discrete Models