Analysis of long-time interaction of perturbations in problems of macrokinetics

Abstract

We developed an approach for the reduction of systems of nonlinear partial differential equations to the general nonlinear parabolic equation for a complex amplitude of an envelope wave. The equation is complexly derived: by using wave packages, method of many scales, modification of Mandelshtam method and taking into account group velocity of an envelope wave, that is typical for an actual nonlinear dispersive medium. We consider the features of such modeling for a system with nonlinearities occurring in the simplest model of a nonisothermal chemical reaction, in particular, of thermal autoignition and flame propagation.