Enhancing and essentially generalizing previous results on a class of (1+ 1)-dimensional
nonlinear wave and elliptic equations, we apply several new techniques to classify …

We carry out the group classification of the class of two-dimensional shallow water
equations with variable bottom topography using an optimized version of the method of …

In these lectures we review two procedures for constructing finite difference numerical
schemes that preserve symmetries of differential equations. The first approach is based on …

We carry out the extended symmetry analysis of a two-dimensional degenerate Burgers
equation. Its complete point-symmetry group is found using the algebraic method, and all its …

We carry out extended symmetry analysis of the (1+ 2)-dimensional Boiti–Leon–Pempinelli
system, which corrects, enhances and generalizes many results existing in the literature …

We exhaustively classify the Lie reductions of the real dispersionless Nizhnik equation to
partial differential equations in two independent variables and to ordinary differential …

We carry out enhanced symmetry analysis of a two-dimensional Burgers system. The
complete point symmetry group of this system is found using an enhanced version of the …

Applying an original megaideal-based version of the algebraic method, we compute the
point-symmetry pseudogroup of the dispersionless (potential symmetric) Nizhnik equation …

Using the original advanced version of the direct method, we efficiently compute the
equivalence groupoids and equivalence groups of two peculiar classes of Kolmogorov …

We classify the admissible transformations in a class of variable coefficient Korteweg–de
Vries equations. As a result, a full description of the structure of the equivalence groupoid of …