Small amplitude approximation and stabilities for dislocation motion in superlattice

Starting from the traveling wave solution, in small amplitude approximation, Sine-Gordon equation can be reduced to a generalized Duffing equation to describe the dislocation motion in superlattice, and the phase plane properties of system phase plane are described in the absence of applied field, the stabilities are also discussed in the presence of applied field. It is pointed out that the separatrix orbit describing the dislocation motion as the kink wave may transfer the energy along the dislocation line, keep its form unchanged, and reveal the soliton wave properties of the dislocation motion. It is stressed that the dislocation motion process is the energy transfer and release process, and the system is stable when its energy is minimum.