Directed Burgers waves interacting with mean field the modified Burgers equation and its stationary solutions

Projecting technique is used for a system of coupled
nonlinear equations for interacting modes derivation. Three independent modes of
the viscous flow: leftwards, rightwards propagating (acoustic) and the
stationary one (heat) are specified by a set of orthogonal projectors. The final
system of coupled equations is equivalent to the basic one with the accuracy up
to the third-order nonlinear terms and its form allows to apply nonsingular
perturbations method for an approximate solution in the case when one mode is
dominant compared with other iterated modes. Caloric and thermal equations of
state are taken in the general form. Thermoviscous media are treated, that leads
to a system of coupled equations of the Burgers type. The modified Burgers
equation for rightwards mode affected by other ones is obtained as well as its
stationary solutions.