One considers a class of PDEs systems (1) equivalent to (8) and one determines the PDEs system (10) which defines the associated symmetry group. Particularly, for the Blair system (2)+(3) equivalent to (14), one finds the symmetry Lie group G (Theorem 5). One proves that the class of PDEs systems in the form (8)+(14′) which are invariant with respect to the Lie group G, is reduced to the Blair ...

In this paper we compute the charge group for symmetry preserving D-branes on group manifolds for all simple, simply-connected, connected compact Lie groups G.

Hidden symmetries of ordinary differential equations (ODEs) are studied with nonlocal group generators. General forms are given for an exponential nonlocal group generator of an ODE that is reduced from a higher-order ODE, which is expressed in canonical variables and which is invariant under a two-parameter Lie group. The nonlocal group generator identifies a type I hidden symmetry. Type II hi...

New exact solutions are obtained for several nonlinear physical equations, namely the Navier–Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schrödinger equation. The solution methods make use of the symmetry group of the system in situations when the standard Lie method of symmetry reduction is not applicable.

We find a new quantum Yangian symmetry of the AdS/CFT S-matrix, which complements the original su(2|2) symmetry to gl(2|2) and does not have a Lie algebra analog. Our finding is motivated by the Yangian double structure discovered at the classical level. [email protected] [email protected] [email protected]