Group classification of variable coefficient quasilinear reaction-diffusion equations

Enhanced Group Analysis and Conservation Laws of Variable Coefficient Reaction–Diffusion Equations with Power Nonlinearities

A class of variable coefficient (1+1)-dimensional nonlinear reaction–diffusion equations of the general form f(x)ut = (g(x)u nux)x + h(x)u m is investigated. Different kinds of equivalence groups are constructed including ones with transformations which are nonlocal with respect to arbitrary elements. For the class under consideration the complete group classification is performed with respect ...

Conservation Laws of Variable Coefficient Diffusion–Convection Equations

We study local conservation laws of variable coefficient diffusion–convection equations of the form f(x)ut = (g(x)A(u)ux)x + h(x)B(u)ux. The main tool of our investigation is the notion of equivalence of conservation laws with respect to the equivalence groups. That is why, for the class under consideration we first construct the usual equivalence group G∼ and the extended one Ĝ∼ including tran...

The extended Riccati equation mapping method for variable-coefficient diffusion-reaction and mKdV equations

Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

X iv :0 70 8. 34 57 v2 [ m at hph ] 1 5 O ct 2 00 7 Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source O.O. Vaneeva†1, R. O. Popovych†‡2 and C. Sophocleous§3 † Institute of Mathematics of National Academy of Sciences of Ukraine, 3 Tereshchenkivska Str., Kyiv-4, 01601 Ukraine ‡ Fakultät für Mathematik, Universität Wien, Nordberg...

Enhanced Group Analysis of Variable Coefficient Semilinear Diffusion Equations with a Power Source

X iv :0 70 8. 34 57 v1 [ m at hph ] 2 6 A ug 2 00 7 Enhanced Group Analysis of Variable Coefficient Semilinear Diffusion Equations with a Power Source O.O. Vaneeva†1, R. O. Popovych†‡2 and C. Sophocleous§3 † Institute of Mathematics of National Academy of Sciences of Ukraine, 3 Tereshchenkivska Str., Kyiv-4, 01601 Ukraine ‡ Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, A-1090 Wi...