Nonlinear wave equations for chemical reactions with diffusion in multicomponent systems

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Abstract
From the conservation equations for the particle densities and the momentum densities of an arbitrary number of chemically reacting components, coupled, nonlinear wave equations are derived for the particle densities which describe the spatial and temporal change of each species as a result of reactions and diffusion. The coupled steady-state equations are reduced to a nonlinear reaction–diffusion equation for one component and linear Laplace equations for the other components. As applications, the dynamics of (i) fast reactive waves propagating with thermal speed, (ii) slow chemical waves propagating at infrasonic speeds, and (iii) the damping of the Lotka oscillations are analyzed within the frame of the hyperbolic theory. It is shown that the hyperbolic diffusion theory is free from the physical and mathematical deficiencies of the phenomenological (parabolic) diffusion theory.