| Summary: | 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. Keywords: Nematic liquid crystals, Sine-Gordon equation, Kink and anti-kink Sine-Gordon solitons
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