Abstract Infinitesimal symmetries of a partial differential equation (PDE) can be defined algebraically as the solutions linearisation (Frechet derivative) holding on space to PDE, and they are well-known comprise linear having structure Lie algebra. Solutions adjoint PDE called adjoint-symmetries. Their algebraic for general systems is studied herein. This motivated by correspondence between v...

Generalized mechanics where the Lagrangian describing the system depends on higher order derivatives has been investigated in connection with relativistic dynamics of particles, supersymmetry, polymer physics, string models and gravity theory, among other problems (see, e.g., [11]). For instance, it has been proposed to add to the point particle action a term proportional to acceleration, or th...

Taking the Stückelberg Lagrangian associated with the abelian selfdual model of P. K. Townsend et al as a starting point, we embed this mixed firstand second-class system into a pure first-class system by following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin. The resulting Lagrangian possesses an extended gauge invariance and provides a non-trivial example...

We consider symmetries and perturbed of canonical Hamiltonian equations motion. Specifically we the case in which exhibit a ?-symmetry under some Lie point vector field. After brief survey relationships between standard existence first integrals, recall definition properties ?-symmetries. show that presence for equations, one can introduce notion ?-constant The leads also to nice useful reducti...

We derive a Lagrangian based approach to study the compatible Hamiltonian structure of the dispersionless KdV and supersymmetric KdV hierarchies and claim that our treatment of the problem serves as a very useful supplement of the so-called r-matrix method. We suggest specific ways to construct results for conserved densities and Hamiltonian operators. The Lagrangian formulation, via Noether’s ...