Perturbed soliton and director deformation in a ferronematic liquid crystal

Highlights: • The ferronematic liquid crystal is investigated for soliton dynamics. • The dynamics of the combined system is governed by sine Gordon equation. • The sine Gordon equation is solved for the soliton solution. • Numerical simulation is used for the soliton excitations. - Abstract: The nonlinear molecular deformation of the ferronematic liquid crystal in the presence of external applied magnetic field intensity is investigated in view of solitons for the director axis. The Frank's free energy density of the nematic liquid crystal comprising the basic elastic deformations, molecular deformation associated with the nematic molecules and the suspended ferromagnetic particles and their interactions with magnetic field intensity is deduced to a sine-Gordon like equation using the classical Euler–Lagrange's equation. Using the small angle approximation we establish the Ginzburg–Landau (GL) equation and a class of solutions are obtained. In the normal condition of large angle oscillation of the director axis, we constructed a damped sine-Gordon (sG) equation with the additional perturbation appears in the form of cosine function. The sG equation is solved using numerical simulation and kink excitations were obtained as the molecular deformation for the case of constant damping and distorted kink to a planar configuration transition as we increase the damping.