Generalized Sine-Gordon equation and dislocation dynamics of superlattice

By introducing a damping term, the Seeger equation describing the dislocations motion is reduced to the generalized Sine-Gordon equation, which is further reduced to the pendulum equation for the traveling wave solutions. The characteristics of the phase plane of the unperturbated system is analyzed and the chaotic behavior of the system is discussed with Melnikov method. It is shown that the energy of dislocation wave can efficiently transfer and release to the superlattice for appropriately chosen parameters, such that the stability of the superlattice can be improved.