Abstract
We have constructed a general nonlinear parabolic equation for an autocatalytic reaction-diffusion model. This equation for the complex amplitude of the envelope wave allows one to analyze the long-term behavior of the system after a loss of stability. The coefficients of the equation of this system are explicitly expressed through parameters of the original full Brusselator model with diffusion. The amplitude equation takes into account the possibility of locating the center of the wave packet out the harmonics with maximum increment.
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