Low-dimensional modelling of a generalised Burgers equation

Abstract

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 1-mode and 2-mode centre manifold models of the generalized Burgers equations for bounded smooth time dependent coefficients. These modelings give some interesting extensions to existing results such as the similarity solutions using the similarity method.