The Lie theorem for Birkhoffian systems with time-scale nonshifted variational problems are studied, including free system, generalized system and constrained system. First, the Pfaff-Birkhoff principle is established, dynamical equations three under deduced. Afterwards, in problems, by introducing infinitesimal transformations, symmetry defined respectively. Then theorems kinds of deduced prov...

In the present paper, seventh order Caudrey-Dodd-Gibbon (CDG) equation is solved by Lie symmetry analysis. All geometry vector fields of KdV equations are presented. Using transformation CDG reduced into ordinary differential equations. These ODEs power series method to obtain exact solution. The convergence also discussed.

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.