Sine-Gordon Solitons In Namatic Liquid Crystals

A soliton is a self-reinforcing solitary wave that maintains its shape while it propagates at a constant velocity. And soliton phenomenon is an important rearch interest in nonlinear physics. Nematic liquid crystals are wonderful nonlinear nonlocal systems well suited for several experimental and theoretical investigations. In this dissertation, the Sine-Gordon soliton for nematic liquid crystal molecule’s rotation reorientation in electric filed and magnetic field is investigated theoretically.From the theory of nematic liquid crystal interact with electric field and the onedimensional monatomic chain model, the Sine-Gordon equation suits for molecule’s rotation motion is derived. According to initial condition and boundary condition, a couple of double kink-soliton(anti-kink soliton) and a breather are calculated theoretically. The shape of kink-solitary waves propagating in nematic liquid crystal and breather are simulated respectively. The effect of the external applied electric field on kink-soliton’s shape and propagation as well as breather’s breath frequency are discussed. Besides, the essence of breather is concluded that it’s an oscillation as a result of collision between kink-soliton and anti-kink soliton.With the same method used in molecule’s interaction with electric field, the motion equation of molecules interact with magnetic field is derived. A couple of kink-solitons and a breather which can exist under magnetic field’s interaction are also theoretically figured out. The kink-solitons’ propagation and breather’s breath frequency influenced by magnetic field is analyzed. And the kink-solitons and breather is compared with the case in electric field.At last, the equation that nematic liquid crystal molecules interact with electric field and magnetic field is derived. The solution for the motion equation calculated by Jacobi elliptic function F-method is still a couple kink-solitons. The analysis of the external field’s influence indicates that the kink-solitons’ shape and propagating velocity is totally determined by the applied electric field and magnetic field.