Indeed, these symmetries differ from the Lie derivative only by a gauge transformation and are often called improved diffeomorphisms @1#. If the only symmetries of the ChernSimons action are the diffeomorphisms ~3! and the gauge transformations ~2!, then we shall say that there is no accidental gauge symmetry. How this translates into an algebraic condition on ga1•••an11 will be described preci...

Group-theoretic methods based on local symmetries are useful to construct invariant solutions of PDEs and to linearize nonlinear PDEs by invertible mappings. Local symmetries include point symmetries, contact symmetries and, more generally, Lie-Biicklund symmetries. An obvious limitation in their utility for particular PDEs is the non-existence of local symmetries. A given system of PDEs with a...

Additional nonlocal symmetries of diffusion-convection equations and the Burgers equation are obtained. It is shown that these equations are connected via a generalized hodograph transformation and appropriate nonlocal symmetries arise from additional Lie symmetries of intermediate equations. Two entirely different techniques are used to search nonlocal symmetry of a given equation: the first i...

A complete classification of generalized symmetries of the Yang-Mills equations on Minkowski space with a semi-simple structure group is carried out. It is shown that any generalized symmetry, up to a generalized gauge symmetry, agrees with a first order symmetry on solutions of the Yang-Mills equations. Let g = g1+ · · ·+gn be the decomposition of the Lie algebra g of the structure group into ...

Lie and conditional symmetries of nonlinear diffusion equations with convection term are described. Examples of new ansätze and exact solutions are presented.

We study the Lie point symmetries of semilinear Kohn-Laplace equations on the Heisenberg group H and obtain a complete group classification of these equations.

We construct explicitly the symmetries of the isospectral deformations as twists of Lie algebras and generalize the deformation for an arbitrary twist.

*Correspondence: [email protected] 1College of Mathematics, China University of Mining and Technology, Xuzhou, 221116, P.R. China Full list of author information is available at the end of the article Abstract The symmetry analysis method is used to study the Drinfeld-Sokolov-Wilson system. The Lie point symmetries of this system are obtained. An optimal system of one-dimensional subalgebras ...

Understanding the exceptional Lie groups as the symmetry groups of simpler objects is a longstanding program in mathematics. Here, we explore one famous realization of the smallest exceptional Lie group, G2. Its Lie algebra g2 acts locally as the symmetries of a ball rolling on a larger ball, but only when the ratio of radii is 1:3. Using the split octonions, we devise a similar, but more globa...

The Lie group method is used in order to investigate various issues related to symmetries and exact solutions of the barotropic vorticity equation. This is done in a similar but more systematic and complete way as given by Huang and Lou [Phys. Lett. A. 320 (2004) 428–437]. The Lie symmetries of the barotropic vorticity equations on the f and β-planes as well as on the sphere in rotating and res...