Renat Zhdanov (BIO-key International, USA) and Viktor Lahno (Poltava State Pedagogical University, Ukraine)

Symmetry classification of the general second-order (1+1)-dimensional evolution equation

We develop the generic approach to a complete solution of the group classification problem for the general second-order evolution equation. It enables us to classify all inequivalent equations in question admitting non-trivial Lie symmetries. As a by-product, we get a novel classification of quasi-local symmetries of quasi-linear evolution equations. So that we constructed broad classes of PDEs admitting non-point symmetry groups.