Low-dimensional modelling of a generalized Burgers equation

Details Low-dimensional modelling of a generalized Burgers equation Low-dimensional modelling of a generalized Burgers equation

2003-07-30

arxiv.org/abs/math-ph/0307064v1

Physics

Mathematical Physics

15 pages

Scientific paper

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.

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