New results on group classification of nonlinear diffusion-convection equations

Details New results on group classification of nonlinear diffusion-convection equations New results on group classification of nonlinear diffusion-convection equations

2003-06-12

arxiv.org/abs/math-ph/0306035v4

J. Phys. A: Math. Gen., 2004, V.37, N 30, 7547-7565

Physics

Mathematical Physics

LaTeX2e, 19 pages

Scientific paper

10.1088/0305-4470/37/30/011

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient $(1+1)$-dimensional nonlinear diffusion-convection equations of the general form $f(x)u_t=(D(u)u_x)_x+K(u)u_x.$ We obtain new interesting cases of such equations with the density $f$ localized in space, which have large invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local trasformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.

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