A novel method is presented for solving the forced transient diffusion flame in the exit region of a coflow burner. Streamwise diffusion is eliminated, which produces the Burke-Schumann model. A mathematical transformation renders the transient, forced convection problem equivalent to a steady-state convection problem. The transformation differs from previous approaches because its use does not require a priori restriction to small perturbations. For this reason, flow fluctuations that are large fractions of the initial flow field may be described exactly and features of nonlinear response can be examined without recourse to detailed numerical simulation. The method is applied to study flame evolution and oscillation for two physically separated coflow slot burner flames as they merge. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.