  A nonlinear equation describing curved stationary flames with arbitrary gas
expansion $\theta = \rho_{{\rm fuel}}/\rho_{{\rm burnt}}$, subject to the
Landau-Darrieus instability, is obtained in a closed form without an assumption
of weak nonlinearity. It is proved that in the scope of the asymptotic
expansion for $\theta \to 1,$ the new equation gives the true solution to the
problem of stationary flame propagation with the accuracy of the sixth order in
$\theta - 1.$ In particular, it reproduces the stationary version of the
well-known Sivashinsky equation at the second order corresponding to the
approximation of zero vorticity production. At higher orders, the new equation
describes influence of the vorticity drift behind the flame front on the front
structure. Its asymptotic expansion is carried out explicitly, and the
resulting equation is solved analytically at the third order. For arbitrary
values of $\theta,$ the highly nonlinear regime of fast flow burning is
investigated, for which case a large flame velocity expansion of the nonlinear
equation is proposed.
