The Sine-Gordon solitons in nematic liquid crystals under the external electric field

In this paper, we study the dynamic equation of molecular motion in nematic liquid crystals when there exists the twisting disturbance of the molecular arrangement under the external electric field. After a series of derivation, we find that the evolution equation satisfies the form of Sine-Gordon equation which indicates that the molecular twisting deformation may propagate in the form of solitary waves under external electric field, and the kink and anti-kink Sine-Gordon solitary solutions are given then. The existence of a couple of kink and anti-kink Sine-Gordon solitons in nematic liquid crystals is proved. And we also discuss the influence of the velocity of the traveling wave on the solitary propagation.