In this paper Mathematical structure of time-dependent Lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent Lagrangian systems are considered. Starting point is time-independent Lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to th...

in this paper mathematical structure of time-dependent lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent lagrangian systems are considered. starting point is time-independent lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to the...

we introduce a new solution for kawahara-kdv equations. the lie group analysis is used to carry out the integration of this equations. the similarity reductions and exact solutions are obtained based on the optimal system method.

In this work, we consider the Lie's method of infinitesimal transformation groups and discrete symmetries method for Burgers equation with time dependent flux at the origin. Following the Lie's method of infinitesimal transformation groups we determine the symmetry reductions and similarity solutions of the governing equation. By applying discrete symmetries analysis we have obtained three grou...

An algebraic method is devised to look for non-local symmetries of the pseudopotential type of nonlinear field equations. The method is based on the use of an infinite-dimensional subalgebra of the prolon-gation algebra L associated with the equations under consideration. Our approach, which is applied by way of example to the Dym and the Korteweg-de Vries equations, allows us to obtain a gener...

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, i.e., at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point...

We consider weakly pseudoconvex hypersurfaces with polynomial models in $${\mathbb {C}}^N$$ and their symmetry algebras. In the most prominent case of special models, given by sums squares polynomials, we give complete classification. particular, prove that such manifolds do not admit any nonlinear symmetries, depending only on complex tangential variables, nor they real or nilpotent linear sym...

A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions. To begin, we analyze symmetries that can be built from the metric, curvature, and covariant derivatives o...