Oleksandr A. Pocheketa (Institute of Mathematics, Kyiv)
Roman O. Popovych (Wolfgang Pauli Institute, Wien, Austria; Institute of Mathematics, Kyiv)

Singular reduction modules of differential equation

Abstract:
Using advanced classification techniques, we carry out the extended symmetry analysis of the class of generalized Burgers equations of the form $u_t+uu_x+f(t,x)u_{xx}=0$. This enhances all the previous results on symmetries of these equations and includes the description of admissible transformations, Lie symmetries, Lie and nonclassical reductions, conservation laws, potential admissible transformations and potential symmetries. The study is based on the fact that the class is normalized, and its equivalence group is finite-dimensional.

This talk is based on the paper arXiv:1603.09377.