  The problem of non-perturbative description of stationary flames with
arbitrary gas expansion is considered. On the basis of the Thomson circulation
theorem an implicit integral of the flow equations is constructed. With the
help of this integral, a simple explicit expression for the vortex mode of the
burnt gas flow near the flame front is obtained. Furthermore, a dispersion
relation for the potential mode at the flame front is written down, thus
reducing the initial system of bulk equations and jump conditions for the flow
variables to a set of integro-differential equations for the flame front
position and the flow velocity at the front. The developed approach is applied
to the case of thin flames. Finally, an asymptotic expansion of the derived
equations is carried out in the case \theta\to 1 where \theta is the gas
expansion coefficient, and a single equation for the front position is obtained
in the second post-Sivashinsky approximation. It is demonstrated, in
particular, how the well-known problem of correct normalization of the front
velocity is resolved in the new approach. It is verified also that in the first
post-Sivashinsky approximation, the new equation reduces to the
Sivashinsky-Clavin equation corrected according to Cambray and Joulin.
Analytical solutions of the derived equations are found, and compared with the
results of numerical simulations.
