text: To neglect the influences by hydrodynamic instabilities such as Darrieus–Landau instability, Rayleigh–Taylor instability etc., the analysis usually neglects effects due to the thermal expansion of the gas mixture by assuming a constant density model. Such an approximation is referred to as diffusive-thermal approximation or thermo-diffusive approximation which was first introudced by Grigory Barenblatt, Yakov Zeldovich and A. G. Istratov in 1962. With a one-step chemistry model and assuming the perturbations to a steady planar flame in the form , where  is the transverse coordinate system perpendicular to flame,  is the time,  is the perturbation wavevector and  is the temporal growth rate of the disturbance, the dispersion relation  for one-reactant flames is given implicitly by
  where , ,  is the Lewis number of the fuel and  is the Zeldovich number. This relation provides in general three roots for  in which the one with maximum  would determine the stability character. The stability margins are given by the following equations
  describing two curves in the vs. plane. The first curve is associated with condition , whereas on the second curve  The first curve separates the region of stable mode from the region corresponding to cellular instability, whereas the second condition indicates the presence of traveling and/or pulsating instability.