Low-dimensional modelling of a generalized Burgers equation

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2007

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Li, Z.
Roberts, A.

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Global Journal of Pure and Applied Mathematics, 2007; 3(3):203-218

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Zhenquan Li and A.J. Roberts

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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 lmode 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.

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