The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...

We construct generalized symmetries for linearized Einstein gravity in arbitrary dimensions. First-principle considerations quantum field theory force to appear dual pairs. Verifying this prediction helps us find the full set of nontrivial conserved charges---associated, equal parts, with 2-form and ($D\ensuremath{-}2$)-form currents. Their total number is $D(D+1)$. compute commutators pairs ch...

In recent years, the notion of symmetry has been extended from classical symmetries to also include constant cofactor symmetries, single variable symmetries and Kronecker symmetries. All these symmetries form a generalized symmetry scheme. Existing methods to detect generalized symmetries require computing the cofactors for each pair of variables to check certain relationships between the cofac...

the purpose of this paper is to analyze in detail a special nonlinear partial differentialequation (npde) of the second order which is important in physical, chemical and technicalapplications. the present npde describes nonlinear diffusion and is of interest in several partsof physics, chemistry and engineering problems alike. since nature is not linear intrinsicallythe nonlinear case is there...

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...

We consider the curvatures 2 form asociated with AdSL4 valued one-form gauge connetion, and then we construct a four-dimensional action that generalize Einstein-Hilbert gravity. It is shown Maxwell extension of Einstein gravity can be obtained from AdSL4-gravity making use Inonu-Wigner contraction method. In same way, by gauging AdSL5 spacetime algebra, extended including vector fields kab ha w...

We present an extension of the methods of classical Lie group analysis of diierential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by Colombeau's theory of algebras of generalized functions. We show that under some mild conditions on the diierential equations, symmetries of classical solutions r...

We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by Colombeau’s theory of algebras of generalized functions. We show that under some mild conditions on the differential equations, symmetries of classical solutions...

A complete and explicit classification of generalized, or local, symmetries of massless free fields of spin s ≥ 1/2 is carried out. Up to equivalence, these are found to consists of the conformal symmetries and their duals, new chiral symmetries of order 2s, and their higher-order extensions obtained by Lie differentiation with respect to conformal Killing vectors. In particular, the results yi...

We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by Colombeau’s theory of algebras of generalized functions. We show that under some mild conditions on the differential equations, symmetries of classical solutions...