Low-dimensional Modeling of a Generalised Burgers Equation

Burgers equation is one of the simplest nonlinear partial differential equations'it combines the basic processes of diffusion and nonlinear steepening. In some applicationsit is appropriate for the diffusion coefficient to be a time-dependent function.Using aWayne's transformation and centre manifold theory, we derive l-mode and2-mode centre manifold models of the generalized Burgers equations for boundedsmooth time dependent coefficients. These modelings give some interesting extensionsto existing results such as the similarity solutions using the similarity method.