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In the context of the large thermal-expansion approximation, we derive an equation describing flame front dynamics under conditions of Darrieus-Landau instability. We show that the second-order theory leads to system of two evolution equations for the flame front perturbations and for the potential of the unburned mixture flow. In the limiting case of long evolution, the system of equations can be reduced to one equation with respect to the additive variable that is the sum of the front perturbations and the flow potential. The equation with respect to the additive variable at large gas expansion coefficients has the form of the Sivashinsky equation obtained for the case of small gas expansion coefficients.

Nonlinear analysis of flame hydrodynamic instability at large gas expansion ratio