The coherent constant and proportional patterns for the equilibrium and nonequilibrium models of adsorption dynamics have been analyzed for linear adsorption isotherms at variable linear fluid velocity in the fixed bed. The Riemann, R(k), and L(i) invariants are found in the simple analytical form. The conditions of existence of the coherent patterns are obtained for the equilibrium and nonequilibrium models. The influence of the dispersive factors (kinetics and longitudinal dispersion) on the nature of the concentrations distributions is considered. For different nonequilibrium theoretical models, the simple formula is derived to calculate the mass transfer zone for the coherent constant patterns. It is shown that the dispersive factors can convert coherent patterns into incoherent ones.