The non-linear dynamics of perturbations of dislocation density and of dislocation charge-density were analyzed in terms of a system of evolution equations. A solitary wave existed in an ensemble of dislocations. It took the form of a jump in the total dislocation density, and the form of a soliton for the excess density. The stability of the self-similar solutions which were found was analyzed. There was found to be a region of parameter values within which steady-state wave solutions were stable. The spectrum of possible values of the propagation velocity of a solitary wave was also found.

Solitary Charge-Density Wave in an Ensemble of Dislocations. I.L.Maksimov, G.F.Sarafanov: Pisma Zhurnal Eksp. Teor. Fiz., 1995, 61[5], 405-11 (JETP Letters, 1995, 61[5], 411-7)