Persistent Propagation of Concentration Waves in Dissipative Media Far from Thermal Equilibrium

The origin of persistent wave propagation through medium of reaction-diffusion type is explored. Our theory is based on a generalized time-dependent Ginzburg-Landau equation for a complex field W, namely, the equation derived previously in connection with the instability problems in nonlinear chemical kinetics. For slow variation of W in space and time the above equation is further reduced to a Navier-Stokes-like one for the phase gradient of W. Under a certain condition, the “viscosity” coefficient becomes negative, and at the same time the temporally ordered state of uniform concentrations becomes unstable. In such a situation we find a particular solution corresponding to a propagating concentration wave with a wave-source or sink.