  Steady premixed flames subjected to space-periodic steady forcing are studied
via inhomogeneous Michelson-Sivashinsky (MS) and then Burgers equations. For
both, the flame slope is posited to comprise contributions from complex poles
to locate, and from a base-slope profile chosen in three classes (pairs of
cotangents, single-sine functions or sums thereof). Base-slope-dependent
equations for the pole locations, along with formal expressions for the
wrinkling-induced flame-speed increment and the forcing function, are obtained
on excluding movable singularities from the latter. Besides exact few-pole
cases, integral equations that rule the pole-density for large wrinkles are
solved analytically. Closed-form flame-slope and forcing-function profiles
ensue, along with flame-speed increment vs forcing-intensity curves; numerical
checks are provided. The Darrieus-Landau instability mechanism allows MS flame
speeds to initially grow with forcing intensity much faster than those of
identically forced Burgers fronts; only the fractional difference in speed
increments slowly decays at intense forcing, which numerical (spectral)
timewise integrations also confirm. Generalizations and open problems are
evoked.
