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

Abstract

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.

14 pages

References in corpus (4)

• Conservation Laws and Potential Symmetries of Linear Parabolic Equations
• Hierarchy of Conservation Laws of Diffusion--Convection Equations
• Group Analysis of Variable Coefficient Diffusion-Convection Equations. II. Contractions and Exact Solutions
• Group Analysis of Variable Coefficient Diffusion--Convection Equations. III. Conservation Laws

Cited by in corpus (1)

• Exact Solutions of Diffusion-Convection Equations