Abstract: It is generally known that classical point and potential Lie symmetries of differential equations (the latter calculated as point symmetries of an equivalent system) can be different. We question whether this is true when the symmetries are extended to nonclassical symmetries. In this paper, we consider two classes of nonlinear partial differential equations; the first one is a diffus...

generalization of Rosenfeld's fuzzy subgroup, and Bhakat and Das's fuzzy subgroup is given in [20]. Lie algebras are so-named in honor of Sophus Lie, a Norwegian mathematician who pioneered the study of these mathematical objects. Lie's discovery was tied to his investigation of continuous transformation groups and symmetries. The structure of the laws in physics is largely based on symmetries....

‎this paper obtains the exact solutions of the wave equation as a second-order partial differential equation (pde)‎. ‎we are going to calculate polynomial and non-polynomial exact solutions by using lie point symmetry‎. ‎we demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎a generalized procedure for polynomial solution is pr...

The discrete symmetries P, C and T are discussed in terms of Lie algebra extensions of the Poincare Lie algebra. This formulation leads to certain problems of Lie algebra theory which will be presented in this and succeeding papers. (To be submitted to Communications in Mathematical Physics) * Work supported by the U. S. Atomic Energy Commission.

In this paper we restrict ourselves to Lie point symmetries an applications to the fourth order generalized Burgers equation GBE4. Using computer programs under the computer algebra package MATHEMATIC A we find a three dimensional solvable Lie algebra of point symmetries of the GBE4 equation. The similarity reductions due to these symmetries have also been obtained. The idea of applying Lie gro...

Higher order symmetry operators for the wave equation with scalar and vector potentials are investigated. All scalar potentials which admit second order symmetry operators are found explicitly. Symmetries of partial differential equations are used for separation of variables [1], description of conservation laws [2], construction of exact solutions [3], etc. Before can be applied, symmetries ha...

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge the...

A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be used to perform symmetry reduction. The method generalizes one presented in a recent publication for the case of ordinary difference equations. In turn, it ...

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differentialdifference equations. As an example of the application of the methods, we construct the discrete symmetries of the discrete Painlevé I equation and of the Toda lattice equation.