Group Analysis of Variable Coefficient Diffusion-Convection Equations. IV. Potential Symmetries

Details Group Analysis of Variable Coefficient Diffusion-Convection Equations. IV. Potential Symmetries Group Analysis of Variable Coefficient Diffusion-Convection Equations. IV. Potential Symmetries

2007-10-23

arxiv.org/abs/0710.4251v1

Physics

Mathematical Physics

14 pages

Scientific paper

This paper completes investigation of symmetry properties of nonlinear variable coefficient diffusion-convection equations of the form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$. Potential symmetries of equations from the considered class are found and the connection of them with Lie symmetries of diffusion-type equations is shown. Exact solutions of the Fujita--Storm equation $u_t=(u^{-2}u_x)_x$ are constructed.

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