In this paper we consider a class of generalized nonlinear hyperbolic partial differential equations of the Hunter–Saxton-Calogero type, which arise in the theory of control of liquid crystals and in the control of unsteady gas flows. We found such conditions that the original equation can be reduced to linear one by contact transformations. The general exact multivalued solutions of the Hunter–Saxton–Calogero equation are found. The obtained solutions are visualized.