  Burgers equation is one of the simplest nonlinear partial differential
equations-it combines the basic processes of diffusion and nonlinear
steepening. In some applications it is appropriate for the diffusion
coefficient to be a time-dependent function. Using a Wayne's transformation and
centre manifold theory, we derive l-mode and 2-mode centre manifold models of
the generalised Burgers equations for bounded smooth time dependent
coefficients. These modellings give some interesting extensions to existing
results such as the similarity solutions using the similarity method.
