Dynamics of cholesteric liquid crystal with variable pitch

We have written expressions for the free energy of a cholesteric liquid crystal in an approximation using the elasticity constants K_1, K_2, K_3 and the energy variation and the corresponding energy and energy gradient along the direction of the director vector n at each lattice point for the lattice model. A feature of this lattice model is the shift of the n components in space relative to each other. An assessment has been made of the error associated with the respective substitution. Such an approach can increase the accuracy of calculations of the energy and dynamics of localized states in liquid crystals on low-density lattices.