This article surveys recent advances in the equivariant approach to the method of moving
frames, concentrating on finite-dimensional Lie group actions. A sampling from the many …

. In this paper the partial preliminary group classification of a class of nonlinear wave
equations was carried out via the classification of one-dimensional Lie symmetry extensions …

Methods for the design of physical parameterization schemes that possess certain
invariance properties are discussed. These methods are based on different techniques of …

We presently generalize existing two-equation Reynolds-averaged Navier–Stokes models
by using recent advances in our understanding of the Lie symmetries of governing …

This work applies new insights into turbulent statistics gained by Lie symmetry analysis to
the closure problem of turbulence. Founded in the mathematics of partial differential …

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 …

The explicit formulation of the general inverse problem on conservation laws is presented for
the first time. Within this problem, one aims to derive the general form of systems of …

We refine the concept of the symmetry group of a geometric object through its symmetry
groupoid, which incorporates both global and local symmetries in a common framework. The …

The research network “Basic Concepts for Convection Parameterization in Weather Forecast
and Climate Models” was organized with European funding (COST Action ES0905) for the …

This paper introduces a new, fully recursive algorithm for computing moving frames and
differential invariants of Lie pseudo-group actions. The recursive method avoids unwieldy …