We investigate Lie symmetries of Einstein’s vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on Einstein’s equations. Instead of setting to zero the coefficients of all independent partial derivatives (which involves a very complicated substitution of Einstei...

This Letter focuses on studying non-Noether symmetries and conserved quantities of the nonconservative dynamical system. Based on the relationships among motion, nonconservative forces and Lagrangian, we present conservation laws on non-Noether symmetries for nonconservative dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry in nonconservative sys...

In this paper, we propose a new approach for improving significantly existing guaranteed integration methods state equations with uncertain initial conditions. We first find tube that encloses the solution of differential equation assuming is known. Then, using Lie symmetries, inflate in order to contain uncertainty associated state. The method shown be efficient on examples coming from reachab...

The symmetry group method is important and widely used in the reduction and construction of explicit solutions of PDEs (partial differential equations). As shown in [1 – 4], the Lie symmetry group method can be used to find explicit solutions of PDEs using symmetry reduction and construction. This method is known as the classical method. By a classical symmetry group of a system of PDEs we mean...

Curvature collineations of a spray manifold induced by the Lie symmetries of the underlying spray are studied. The basic observation is that the Jacobi endomorphism and the Berwald curvature are invariant under these symmetries; this implies the invariance of the further curvature data. Our main technical tool is an appropriate Lie derivative operator along the tangent bundle projection. M.S.C....