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Abstract
Equations of motion of director and velocity of nematic liquid crystals under pressure gradients are derived from the Ericksen-Leslie theory. Under suitable approximations, these coupled equations are reduced to a single (2 + 1) nonlinear partial differential equation for the director angle. Boundary effects are taken into account. Similarity analysis of this equation is presented. Properties of steady-state solutions are discussed. Numerical solutions are obtained. Traveling solutions of the (2 + 1) equation are given numerically showing the existence of solitons propagating along the direction of the pressure gradient (in both directions). Corresponding optical interference patterns of these solitons under both monochromatic and white lights are calculated. Good agreement between our theoretical results and recent experiments are obtained.