  Nonlinear non-stationary equation describing evolution of weakly curved
premixed flames with arbitrary gas expansion, subject to the Landau-Darrieus
instability, is derived. The new equation respects all the conservation laws to
be satisfied across the flame front, as well as correctly takes into account
influence of vorticity, generated in the flame, on the flame front structure
and flame velocity. Analytical solutions of the derived equation are found.

Fluid Dynamics;Classical Physics