Nonstationary contrasting structures in the vicinity of a critical point

Abstract

Evolution equations of the internal transition layer (ITL) have been derived for the reaction-diffusion equation and for a pseudo-parabolic third-order equation with a small parameter in the highest derivatives, which describes different processes in physics, chemistry, biology, and, in particular, the process of magnetic field generation in the turbulent medium. We consider a case where there is a point with a zero velocity of the ITL drift (critical point), while the drift velocity both on the right and on the left of this point does not change its sign. It is shown that in the case of balanced cubic nonlinearity, which is fairly common in physical applications, the ITL drift velocity in the first-order asymptotic expansion in the power of a small parameter is also zero, but the second-order approximation makes it possible to obtain the drift velocity at the critical point. It is demonstrated that ITL crosses the critical point in finite time.