Sine-Gordon Solitons and Breathers in Rod-like Magnetic Liquid Crystals under External Magnetic Field**Supported by the Basic Scientific Research Project of Provincial Colleges and Universities in Heilongjiang Province under Grant No. KJCXZD201723, the Youth Science Foundations of Heilongjiang University under Grant No. QL201606

Abstract

To study the nonlinear phenomena in rod-like magnetic liquid crystals (RMLCs), this paper establishes the dynamic model of molecular motion when giving a twisting disturbance to the molecules under external magnetic field. We find the twist of the molecules under magnetic field can be propagated in the form of a traveling wave. The dynamic equation of the molecular twisting we derived satisfies the form of Sine-Gordon equation. We obtain two solutions of the Sine-Gordon equation by theoretical calculation: the kink and anti-kink solitons and breathers. The characteristics of those solitons and breathers are discussed.